We study the dynamics of token launched on Pump.fun, a Solana-based launchpad platform, to identify the determinants of the token success. Pump.fun employs a bonding curve mechanism to bootstrap initial liquidity possibly leading to graduation to the on-chain market, which can be seen as a token success. We build predictive models of the probability of graduation conditional on the current amount of Solana locked in the bonding curve and a set of explanatory variables that capture structural and behavioral aspects of the launch process. Conditioning the graduation probability on these variables significantly improves its predictive power, providing insights into early-stage market behavior, speculative and manipulative dynamics, and the informational efficiency of bonding-curve-based token launches.

Portfolio optimization under strict cardinality constraints is a combinatorial challenge that defies classical convex optimization techniques, particularly in the context of "Direct Indexing" and ESG-constrained mandates. In the Noisy Intermediate-Scale Quantum (NISQ) era, the Quantum Approximate Optimization Algorithm (QAOA) offers a promising hybrid approach. However, standard QAOA implementations utilizing transverse field mixers often fail to strictly enforce hard constraints, necessitating soft penalties that distort the energy landscape. This paper presents a comprehensive analysis of a constraint-preserving QAOA formulation against Simulated Annealing (SA) and Hierarchical Risk Parity (HRP). We implement a specific QAOA ansatz utilizing a Dicke state initialization and an XY-mixer Hamiltonian that strictly preserves the Hamming weight of the solution, ensuring only valid portfolios of size K are explored. Furthermore, we introduce a Trotterized parameter initialization schedule inspired by adiabatic quantum computing to mitigate the "Barren Plateau" problem. Backtesting on a basket of 10 US equities over 2025 reveals that our QAOA approach achieves a Sharpe Ratio of 1.81, significantly outperforming Simulated Annealing (1.31) and HRP (0.98). We further analyze the operational implications of the algorithm's high turnover (76.8%), discussing the trade-offs between theoretical optimality and implementation costs in institutional settings.

This paper examines the effects of the 2019 universalization of Mexico's Social Pension Program (PAM), one of the country's most expansive and politically salient social programs. The reform simultaneously increased the cash transfer and extended eligibility to all individuals aged 65 and over, regardless of income or contributory pension status. Using nationally representative data from the ENIGH and a triple-differences (DDD) identification strategy, we estimate the causal effect of the universalization on poverty and labor market outcomes. Our empirical approach exploits variation across time (pre- and post-reform), age (eligible vs. ineligible), and pension scheme status (non-contributory vs. contributory), allowing us to separate the effects of expanded eligibility from those of increased benefit levels. We find strong increases in take-up rates and no significant change in overall poverty rates, suggesting that many new beneficiaries were not economically vulnerable. However, we document a surprising increase in extreme poverty, concentrated among low-income elderly who responded to the reform by exiting the labor force. This reduction in labor supply, driven by a significant drop in employment among individuals in the bottom income quartile, suggests that the pension acted as a substitute for labor income rather than a supplement. Taken together, the results highlight the trade-offs inherent in universal pension programs: while broader access reduces administrative exclusion, extending transfers to economically secure individuals may dilute redistributive impacts and generate behavioral responses that offset potential welfare gains.

Formulaic alpha factor mining is a critical yet challenging task in quantitative investment, characterized by a vast search space and the need for domain-informed, interpretable signals. However, finding novel signals becomes increasingly difficult as the library grows due to high redundancy. We propose FactorMiner, a lightweight and flexible self-evolving agent framework designed to navigate this complex landscape through continuous knowledge accumulation. FactorMiner combines a Modular Skill Architecture that encapsulates systematic financial evaluation into executable tools with a structured Experience Memory that distills historical mining trials into actionable insights (successful patterns and failure constraints). By instantiating the Ralph Loop paradigm -- retrieve, generate, evaluate, and distill -- FactorMiner iteratively uses memory priors to guide exploration, reducing redundant search while focusing on promising directions. Experiments on multiple datasets across different assets and Markets show that FactorMiner constructs a diverse library of high-quality factors with competitive performance, while maintaining low redundancy among factors as the library scales. Overall, FactorMiner provides a practical approach to scalable discovery of interpretable formulaic alpha factors under the "Correlation Red Sea" constraint.

Industrial symbiosis fosters circularity by enabling firms to repurpose residual resources, yet its emergence is constrained by socio-spatial frictions that shape costs, matching opportunities, and market efficiency. Existing models often overlook the interaction between spatial structure, market design, and adaptive firm behavior, limiting our understanding of where and how symbiosis arises. We develop an agent-based model where heterogeneous firms trade byproducts through a spatially embedded double-auction market, with prices and quantities emerging endogenously from local interactions. Leveraging reinforcement learning, firms adapt their bidding strategies to maximize profit while accounting for transport costs, disposal penalties, and resource scarcity. Simulation experiments reveal the economic and spatial conditions under which decentralized exchanges converge toward stable and efficient outcomes. Counterfactual regret analysis shows that sellers' strategies approach a near Nash equilibrium, while sensitivity analysis highlights how spatial structures and market parameters jointly govern circularity. Our model provides a basis for exploring policy interventions that seek to align firm incentives with sustainability goals, and more broadly demonstrates how decentralized coordination can emerge from adaptive agents in spatially constrained markets.

Improving social welfare is a complex challenge requiring policymakers to optimize objectives across multiple time horizons. Evaluating the impact of such policies presents a fundamental challenge, as those that appear suboptimal in the short run may yield significant long-term benefits. We tackle this challenge by analyzing the long-term dynamics of two prominent policy frameworks: Rawlsian policies, which prioritize those with the greatest need, and utilitarian policies, which maximize immediate welfare gains. Conventional wisdom suggests these policies are at odds, as Rawlsian policies are assumed to come at the cost of reducing the average social welfare, which their utilitarian counterparts directly optimize. We challenge this assumption by analyzing these policies in a sequential decision-making framework where individuals' welfare levels stochastically decay over time, and policymakers can intervene to prevent this decay. Under reasonable assumptions, we prove that interventions following Rawlsian policies can outperform utilitarian policies in the long run, even when the latter dominate in the short run. We characterize the exact conditions under which Rawlsian policies can outperform utilitarian policies. We further illustrate our theoretical findings using simulations, which highlight the risks of evaluating policies based solely on their short-term effects. Our results underscore the necessity of considering long-term horizons in designing and evaluating welfare policies; the true efficacy of even well-established policies may only emerge over time.

The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the surprisal of the market and the Kullback-Leibler divergence between the benchmark-neutral pricing measure and the real-world probability measure. The state variables, their sums, and the growth optimal portfolio of the stocks evolve as squared radial Ornstein-Uhlenbeck processes in respective activity times.

This paper investigates the impact of environmental, social, and governance (ESG) constraint on a regularized mean-variance (MV) portfolio optimization problem in a large-dimensional setting, in which a positive definite regularization matrix is imposed on the sample covariance matrix. We first derive the asymptotic results for the out-of-sample (OOS) Sharpe ratio (SR) of the proposed portfolio, which help quantify the impact of imposing an ESG-level constraint as well as the effect of estimation error arising from the sample mean estimation of the assets' ESG score. Furthermore, to study the influence of the choices of the regularization matrix, we develop an estimator for the OOS Sharpe ratio. The corresponding asymptotic properties of the Sharpe ratio estimator are established based on random matrix theory. Simulation results show that the proposed estimators perform close to the corresponding oracle level. Moreover, we numerically investigate the impact of various forms of regularization matrices on the OOS SR, which provides useful guidance for practical implementation. Finally, based on OOS SR estimator, we propose an adaptive regularized portfolio which uses the best regularization matrix yielding the highest estimated SR (among a set of candidates) at each decision node. Empirical evidence based on the S\&P 500 index demonstrates that the proposed adaptive ESG-constrained portfolio achieves a high OOS SR while satisfying the required ESG level, offering a practically effective approach for sustainable investment.

Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low discrepancy sequences, different sampling strategies, and various analyses of performance. We find that QMC outperforms MC in most cases, including the highest-dimensional simulations, showing faster and more stable convergence. Regarding greeks computation, we compare standard approaches, based on finite differences (FD) approximations, with adjoint methods (AAD) providing evidences that, when the number of greeks is small, the FD approach combined with QMC can lead to the same accuracy as AAD, thanks to increased convergence rate and stability, thus saving a lot of implementation effort while keeping low computational cost. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of QMC simulation, allowed in most cases, but not always, by Brownian Bridge discretization or PCA construction. We conclude that, beyond pricing, QMC is a very effcient technique also for computing risk measures, greeks in particular, as it allows to reduce the computational effort of high dimensional Monte Carlo simulations typical of modern risk management.

We develop a practical framework for identifying and quantifying the hidden layers of risks and optionality embedded in American options by introducing stochasticity into one or more of their underlying determinants. The heuristic approach remedies the problems of conventional pricing systems, which treat some key inputs deterministically, hence systematically underestimate the flexibility and convexity inherent in early-exercise features.

Large Language Models (LLMs) are increasingly integrated into financial workflows, but evaluation practice has not kept up. Finance-specific biases can inflate performance, contaminate backtests, and make reported results useless for any deployment claim. We identify five recurring biases in financial LLM applications. They include look-ahead bias, survivorship bias, narrative bias, objective bias, and cost bias. These biases break financial tasks in distinct ways and they often compound to create an illusion of validity. We reviewed 164 papers from 2023 to 2025 and found that no single bias is discussed in more than 28 percent of studies. This position paper argues that bias in financial LLM systems requires explicit attention and that structural validity should be enforced before any result is used to support a deployment claim. We propose a Structural Validity Framework and an evaluation checklist with minimal requirements for bias diagnosis and future system design. The material is available at https://github.com/Eleanorkong/Awesome-Financial-LLM-Bias-Mitigation.

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses.

Factor Engine is a high-performance, open-source Python library designed for the systematic computation and analysis of financial factors. Built around a modular and extensible API that leverages Python decorators, Factor Engine enables users to define custom factors with ease and integrates seamlessly with the modern data science ecosystem. To assess its practical effectiveness, we compare the mispricing factors computed by Factor Engine to those generated using a reference Stata implementation, finding that both approaches yield highly similar results and comparable performance in backtesting analyses. Furthermore, we experimentally apply these factors within machine learning workflows for trading strategy development, illustrating their practical utility and potential for quantitative finance research.

We introduce the Aggregated Systemic Risk Index (ASRI), comprising four weighted sub-indices: Stablecoin Concentration Risk (30%), DeFi Liquidity Risk (25%), Contagion Risk (25%), and Regulatory Opacity Risk (20%). Using data from DeFi Llama, Federal Reserve FRED, and on-chain analytics, we validate against four historical crises (Terra/Luna, Celsius/3AC, FTX, SVB). Event study analysis detects significant abnormal signals for all four (t-statistics 5.47-32.64, p < 0.01), with threshold-based detection achieving 30-day average lead time for three of four events. Walk-forward validation confirms 4/4 out-of-sample detection (18-day average lead), ruling out look-ahead bias. A three-regime HMM identifies distinct risk states with >97% persistence; structural stability tests pass (Chow p = 0.993). Benchmarking against Diebold-Yilmaz connectedness shows equivalent detection (75%) with higher precision (33.5% vs. 22.4%). Out-of-sample specificity testing on 2024-2025 data confirms zero false positives, correctly classifying the $1.5B Bybit hack as non-systemic. ASRI captures DeFi-specific vulnerabilities -- composability risk, flash loan exposure, and tokenized RWA linkages -- that SRISK and CoVaR cannot accommodate.

Accurate probabilistic forecasting of intraday electricity prices is critical for market participants to inform trading decisions. Existing studies rely on specific domain features, such as Volume-Weighted Average Price (VWAP) and the last price. However, the rich information in the orderbook remains underexplored. Furthermore, these approaches are often developed within a single country and product type, making it unclear whether the approaches are generalizable. In this paper, we extract 384 features from the orderbook and identify a set of powerful features via feature selection. Based on selected features, we present a comprehensive benchmark using classical statistical models, tree-based ensembles, and deep learning models across two countries (Germany and Austria) and two product types (60-min and 15-min). We further perform a systematic generalization study across countries and product types, from which we reveal an asymmetric generalization phenomenon: models trained on more liquid markets or products transfer well to less liquid ones, whereas the reverse transfer leads to substantial performance degradation.

Reinforcement Learning has emerged as a promising framework for developing adaptive and data-driven strategies, enabling market makers to optimize decision-making policies based on interactions with the limit order book environment. This paper explores the integration of a reinforcement learning agent in a market-making context, where the underlying market dynamics have been explicitly modeled to capture observed stylized facts of real markets, including clustered order arrival times, non-stationary spreads and return drifts, stochastic order quantities and price volatility. These mechanisms aim to enhance stability of the resulting control agent, and serve to incorporate domain-specific knowledge into the agent policy learning process. Our contributions include a practical implementation of a market making agent based on the Proximal-Policy Optimization (PPO) algorithm, alongside a comparative evaluation of the agent's performance under varying market conditions via a simulator-based environment. As evidenced by our analysis of the financial return and risk metrics when compared to a closed-form optimal solution, our results suggest that the reinforcement learning agent can effectively be used under non-stationary market conditions, and that the proposed simulator-based environment can serve as a valuable tool for training and pre-training reinforcement learning agents in market-making scenarios.

We investigate multi-period mean-risk portfolio optimization for long-horizon Defined Contribution plans, focusing on buffered Probability of Exceedance (bPoE), a more intuitive, dollar-based alternative to Conditional Value-at-Risk (CVaR). We formulate both pre-commitment and time-consistent Mean-bPoE and Mean-CVaR portfolio optimization problems under realistic investment constraints (e.g., no leverage, no short selling) and jump-diffusion dynamics. These formulations are naturally framed as bilevel optimization problems, with an outer search over the shortfall threshold and an inner optimization over rebalancing decisions. We establish an equivalence between the pre-commitment formulations through a one-to-one correspondence of their scalarization optimal sets, while showing that no such equivalence holds in the time-consistent setting. We develop provably convergent numerical schemes for the value functions associated with both pre-commitment and time-consistent formulations of these mean-risk control problems. Using nearly a century of market data, we find that time-consistent Mean-bPoE strategies closely resemble their pre-commitment counterparts. In particular, they maintain alignment with investors' preferences for a minimum acceptable terminal wealth level-unlike time-consistent Mean-CVaR, which often leads to counterintuitive control behavior. We further show that bPoE, as a strictly tail-oriented measure, prioritizes guarding against catastrophic shortfalls while allowing meaningful upside exposure, making it especially appealing for long-horizon wealth security. These findings highlight bPoE's practical advantages for Defined Contribution investment planning.

Recent advancements in generative AI, such as ChatGPT, have dramatically transformed how people access information. Despite its powerful capabilities, the benefits it provides may not be equally distributed among individuals, a phenomenon referred to as the digital divide. Building upon prior literature, we propose two forms of digital divide in the generative AI adoption process: (i) the learning divide, capturing individuals' heterogeneous abilities to update their perceived utility of ChatGPT; and (ii) the utility divide, representing differences in individuals' actual utility derived from per use of ChatGPT. To evaluate these two divides, we develop a Bayesian learning model that incorporates heterogeneities in both the utility and signal functions. Leveraging a large-scale clickstream dataset, we estimate the model and find significant learning and utility divides across various social characteristics. Interestingly, individuals without any college education, non-white individuals, and those with lower English literacy derive larger utility gains from ChatGPT, yet update their beliefs about its utility at a slower rate. Furthermore, males, younger individuals, and those in occupations with greater exposure to generative AI not only obtain higher utility per use from ChatGPT but also learn about its utility more rapidly. Besides, we document a phenomenon termed the belief trap, wherein users underestimate ChatGPT's utility, opt not to use the tool, and thereby lack new experiences to update their perceptions, leading to continued underutilization. Our simulation further demonstrates that the learning divide can significantly affect the probability of falling into the belief trap, another form of the digital divide in adoption outcomes (i.e., outcome divide); however, offering training programs can alleviate the belief trap and mitigate the divide.

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth trend with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning (STIML) framework that integrates a scaling-based growth model to capture the mechanism-driven average trend, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat annual financial statement data (1950--2019) for 31,553 North American companies, we extend the growth model beyond assets to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth exhibits a clear separation between trend-driven predictability and fluctuation-driven predictability, with their relative importance depending strongly on company size and volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond simple autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic models.

We provide a unified framework to obtain numerically certain quantities, such as the distribution function, absolute moments and prices of financial options, from the characteristic function of some (unknown) probability density function using the Fourier-cosine expansion (COS) method. The classical COS method is numerically very efficient in one-dimension, but it cannot deal very well with certain integrands in general dimensions. Therefore, we introduce the damped COS method, which can handle a large class of integrands very efficiently. We prove the convergence of the (damped) COS method and study its order of convergence. The method converges exponentially if the characteristic function decays exponentially. To apply the (damped) COS method, one has to specify two parameters: a truncation range for the multivariate density and the number of terms to approximate the truncated density by a cosine series. We provide an explicit formula for the truncation range and an implicit formula for the number of terms. Numerical experiments up to five dimensions confirm the theoretical results.

The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices. Fudenberg et al. (2015) develop the additive perturbed utility theory to explain the preference for randomization in the static setting, which, however, becomes ill-posed or intractable in the dynamic setting. We introduce the recursive perturbed utility (RPU), a special stochastic differential utility that incorporates an entropy-based preference for randomization into a recursive aggregator. RPU endogenizes the intertemporal trade-off between utilities from randomization and bequest via a discounting term dependent on past accumulated randomization, thereby avoiding excessive randomization and yielding a well-posed problem. In a general Markovian incomplete market with CRRA preferences, we prove that the RPU-optimal portfolio policy (in terms of the risk exposure ratio) is Gaussian and can be expressed in closed form, independent of wealth. Its variance is inversely proportional to risk aversion and stock volatility, while its mean is based on the solution to a partial differential equation. Moreover, the mean is the sum of a myopic term and an intertemporal hedging term (against market incompleteness) that intertwines with policy randomization. Finally, we carry out an asymptotic expansion in terms of the perturbed utility weight to show that the optimal mean policy deviates from the classical Merton policy at first order, while the associated relative wealth loss is of a higher order, quantifying the financial cost of the preference for randomization.

We investigate whether cryptocurrency markets differentiate between infrastructure failures and regulatory enforcement at the return level, complementing a companion conditional variance analysis that finds 5.7 times larger volatility impacts from infrastructure events (p = 0.0008). Using event-level block bootstrap inference on 31 events across Bitcoin, Ethereum, Solana, and Cardano (2019-2025), we find no statistically significant difference in cumulative abnormal returns between infrastructure failures (-7.6%) and regulatory enforcement (-11.1%): the difference of +3.6 pp has p = 0.81 with 95% CI [-25.3%, +30.9%]. This null acquires substantive meaning alongside the companion's highly significant variance result: the same events that produce indistinguishable return responses generate dramatically different volatility signatures. Markets differentiate shock types through the risk channel -- the second moment -- rather than expected returns. The block bootstrap methodology, which resamples entire events to preserve cross-sectional correlation, reveals that prior parametric approaches systematically understate uncertainty by inflating degrees of freedom. Results are robust across eight specifications including permutation tests, leave-one-out analysis, and the Ibragimov-Mueller few-cluster test.

Using the Crypto Fear & Greed Index and Bitcoin daily data, we document that sentiment extremity predicts excess uncertainty beyond realized volatility. Extreme fear and extreme greed regimes exhibit significantly higher spreads than neutral periods -- a phenomenon we term the "extremity premium." Extended validation on the full Fear & Greed history (February 2018--January 2026, N = 2,896) confirms the finding: within-volatility-quintile comparisons show a significant premium (p < 0.001, Cohen's d = 0.21), Granger causality from uncertainty to spreads is strong (F = 211), and placebo tests reject the null (p < 0.0001). The effect replicates on Ethereum and across 6 of 7 market cycles. However, the premium is sensitive to functional form: comprehensive regression controls absorb regime effects, while nonparametric stratification preserves them. We interpret this as evidence that sentiment extremity captures volatility-regime interactions not fully represented by parametric controls -- consistent with, but not conclusively separable from, the F&G Index's embedded volatility component. An agent-based model reproduces the pattern qualitatively. The results suggest that intensity, not direction, drives uncertainty-linked liquidity withdrawal in cryptocurrency markets, though identification of "pure" sentiment effects from volatility remains an open challenge.

This study investigates whether cryptocurrency whitepaper narratives align with empirically observed market factor structure. We construct a pipeline combining zero-shot NLP classification of 38 whitepapers across 10 semantic categories with CP tensor decomposition of hourly market data (49 assets, 17,543 timestamps). Using Procrustes rotation and Tucker's congruence coefficient (phi), we find weak alignment between claims and market statistics (phi = 0.246, p = 0.339) and between claims and latent factors (phi = 0.058, p = 0.751). A methodological validation comparison (statistics versus factors, both derived from market data) achieves significance (p < 0.001), confirming the pipeline detects real structure. The null result indicates whitepaper narratives do not meaningfully predict market factor structure, with implications for narrative economics and investor decision-making. Entity-level analysis reveals specialized tokens (XMR, CRV, YFI) show stronger narrative-market correspondence than broad infrastructure tokens.

Emerging techniques in computer science make it possible to "brain scan" large language models (LLMs), identify the plain-English concepts that guide their reasoning, and steer them while holding other factors constant. We show that this approach can map LLM-generated economic forecasts to concepts such as sentiment, technical analysis, and timing, and compute their relative importance without reducing performance. We also show that models can be steered to be more or less risk-averse, optimistic, or pessimistic, which allows researchers to correct or simulate biases. The method is transparent, lightweight, and replicable for empirical research in the social sciences.

Time series forecasting is a key tool in financial markets, helping to predict asset prices and guide investment decisions. In highly volatile markets, such as cryptocurrencies like Bitcoin (BTC) and Ethereum (ETH), forecasting becomes more difficult due to extreme price fluctuations driven by market sentiment, technological changes, and regulatory shifts. Traditionally, forecasting relied on statistical methods, but as markets became more complex, deep learning models like LSTM, Bi-LSTM, and the newer FinBERT-LSTM emerged to capture intricate patterns. Building upon recent advancements and addressing the volatility inherent in cryptocurrency markets, we propose a hybrid model that combines Bidirectional Long Short-Term Memory (Bi-LSTM) networks with FinBERT to enhance forecasting accuracy for these assets. This approach fills a key gap in forecasting volatile financial markets by blending advanced time series models with sentiment analysis, offering valuable insights for investors and analysts navigating unpredictable markets.

Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore, analytical expressions for optimal portfolios are always preferred. In our work, we study portfolio optimization problems under the expected utility criterion for a wide range of utility functions, assuming return vectors follow hyperbolic distributions. Our main result demonstrates that under this setup, the two-fund monetary separation holds. Specifically, an individual with any utility function from this broad class will always choose to hold the same portfolio of risky assets, only adjusting the mix between this portfolio and a riskless asset based on their initial wealth and the specific utility function used for decision making. We provide explicit expressions for this mutual fund of risky assets. As a result, in our economic model, an individual's optimal portfolio is expressed in closed form as a linear combination of the riskless asset and the mutual fund of risky assets. Additionally, we discuss expected utility maximization problems under exponential utility functions over any domain of the portfolio set. In this part of our work, we show that the optimal portfolio in any given convex domain of the portfolio set either lies on the boundary of the domain or is the unique globally optimal portfolio within the entire domain.

We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits a sharp additive decomposition that separates nonlinear characteristic discovery from the pricing rule that aggregates them. The economically relevant component of this decomposition is governed by a new object, the Portfolio Tangent Kernel (PTK), which captures the features learned by the network and induces an explicit linear factor pricing representation for the SDF. In population, the PTK-implied SDF converges to a ridge-regularized version of the true SDF, with the effective strength of regularization determined by the spectral complexity of the PTK. Using U.S. equity data, we show that the PTK representation delivers large and statistically significant performance gains, while its spectral complexity has risen sharply-by roughly a factor of six since the early 2000s-imposing increasingly tight limits on finite-sample pricing performance.

We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. The agent under consideration is a price taker who has access only to the stock and factor value processes and the instantaneous volatility. We propose an auxiliary problem in which the agent can invoke policy randomization according to a specific class of Gaussian distributions, and prove that the mean of its optimal Gaussian policy solves the original Merton problem. With randomized policies, we are in the realm of continuous-time reinforcement learning (RL) recently developed in Wang et al. (2020) and Jia and Zhou (2022a, 2022b, 2023), enabling us to solve the auxiliary problem in a data-driven way without having to estimate the model primitives. Specifically, we establish a policy improvement theorem based on which we design both online and offline actor-critic RL algorithms for learning Merton's strategies. A key insight from this study is that RL in general and policy randomization in particular are useful beyond the purpose for exploration -- they can be employed as a technical tool to solve a problem that cannot be otherwise solved by mere deterministic policies. At last, we carry out both simulation and empirical studies in a stochastic volatility environment to demonstrate the decisive outperformance of the devised RL algorithms in comparison to the conventional model-based, plug-in method.

This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the definition of market-based average return of trades during the averaging period. Then we derive the dependence of market-based volatility and higher statistical moments of returns on statistical moments, volatilities, and correlations of the current and past trade values. We derive the approximations of the characteristic function and the probability of returns by a finite number q of market-based statistical moments. To forecast market-based average and volatility of returns at horizon T, one should predict the first two statistical moments and correlation of current and past trade values at the same horizon. We discuss the economic reasons that limit the number of predicted statistical moments of returns by the first two. That limits the accuracy of the forecasts of probability of returns by the accuracy of the Gaussian approximations. To improve the reliability of large macroeconomic and market models like BlackRock's Aladdin, JP Morgan, and the U.S. Fed., the developers should use market-based statistical moments of returns.