Agentic AI systems combine probabilistic reasoning with delegated action through tools, context, memory, orchestration, and external workflow integration. This note develops a formal and managerially usable model that distinguishes Agentic Technical Debt from Stochastic Tax. Agentic Technical Debt is a stock of accumulated design and governance liability. Stochastic Tax is a recurring flow of operating burden that arises when stochastic agents are used in business workflows. The two constructs are related, but they are not the same: debt can amplify the tax, while the tax can remain positive even when debt is minimized. The note starts from a compact dashboard expression, expands it into a fuller structural model, defines all variables and parameters, shows how each cost category can be estimated from operational data, and illustrates the framework with an accounts-payable simulation and companion spreadsheet.

In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic programming problem using deterministic grid methods, which become computationally infeasible for more than a few state variables. In such situations, one needs to rely on simulation methods. The least-squares Monte Carlo (LSMC) method has become a popular simulation method for solving optimal stochastic control problems in quantitative finance over the last decades. In principle, the LSMC, originally developed for pricing Bermudan options, cannot be used directly for pricing variable annuities without simplifying assumptions because the underlying state variables are affected by the control decisions. This paper presents modifications of the LSMC algorithm that makes the pricing of general variable annuities feasible. For numerical illustrations, the pricing of variable annuities with guaranteed minimum withdrawal benefit under optimal withdrawal strategies is obtained with and without stochastic interest rates, using either polynomial regression or neural network regression in the LSMC algorithm. We found that the classical polynomial LSMC can give very accurate prices, at the cost of manual feature engineering, and with a standard deviation of the estimator that increases greatly when interest rates are made stochastic. By contrast, neural network LSMC gives slightly less accurate prices, requires more training time, but does not require manual feature engineering, and making interest rates stochastic makes no visible difference to its accuracy, suggesting a more stable and robust pricing performance of deep LSMC for higher-dimensional pricing problems.

Transition-related financial markets are increasingly exposed to abrupt repricing episodes, elevated volatility, and heterogeneous macro-financial shocks. Under such conditions, conventional Gaussian-linear forecasting frameworks may provide an incomplete representation of the dependence structure linking fossil-energy, renewable-energy, technology, and utility-sector assets. This paper investigates whether transition-related financial returns exhibit residual non-linear predictability after controlling for heavy-tailed multivariate linear dynamics. To address this question, we develop a hybrid forecasting framework combining Student-t Vector Autoregressions with nonlinear recurrent residual learning architectures. The empirical analysis considers six major exchange-traded funds representing broad equity markets and key transition-sensitive sectors. The results reveal substantial departures from Gaussian-linear behavior, including excess kurtosis, volatility clustering, and remaining nonlinear dependence after econometric filtering. Out-of-sample forecasting experiments show that the proposed framework consistently improves predictive accuracy relative to conventional VAR models, standalone machine-learning methods, and alternative hybrid specifications. The forecasting gains become more pronounced during periods of macro-financial stress, particularly during the COVID-19 crisis and the Ukraine-related energy shock. Overall, the findings suggest that transition-related financial systems exhibit regime-sensitive and heavy-tailed predictive dynamics that are insufficiently captured by standard Gaussian-linear models alone.

Ownership concentration is not a scalar. For a normalized investor-stock matrix $A$, it has three irreducible layers: concentration across investors, concentration across stocks, and dependence in the joint assignment of investors to stocks. This paper develops a unified quadratic framework for those layers and shows that the same residual operator that measures static overlap also governs linearized market transmission. Raw micro concentration $M(A) = \sum_{i,j} A_{ij}^2$ admits exact row and column decompositions, support bounds, and fixed-marginal extremal characterizations on the transportation polytope. Benchmark-adjusted dependence $\mathcal{X}(A) = \sum_{i,j} (A_{ij} - p_i s_j)^2 / (p_i s_j)$ admits two exact decompositions: it is a size-weighted average of investor-level deviations from the market portfolio and, symmetrically, of stock-level deviations from the investor base. The paper also proves a multiscale aggregation law: under any partition of investors, total dependence splits exactly into between-group dependence and within-group heterogeneity. Spectrally, $\mathcal{X}(A)$ equals the sum of squared nontrivial singular values of the whitened matrix $D_p^{-1/2} A D_s^{-1/2}$. The residual operator $L$ then yields two dynamic consequences: idiosyncratic fire-sale vulnerability is bounded by the dominant overlap mode $ρ(A)$, while aggregate benchmark-relative alpha variance has worst-case capacity $ρ(A)^2$ and isotropic average-case capacity $\mathcal{X}(A)$. The fixed-marginal geometry also motivates a feasible-range sparsity score that benchmarks observed micro concentration against the sharp minimum and maximum implied by the marginals. The resulting framework separates scale concentration, feasible sparsity, overlap, and linear transmission in a way that is mathematically transparent and empirically usable for work on crowding, fragility, and systemic risk.

Urban decarbonization requires scaling rooftop solar across millions of fragmented producers, yet cities face a fundamental tension: energy data is easily manipulated, and economic incentives often reward speculation rather than actual infrastructure deployment. We present SolarChain, a platform that resolves both problems by anchoring digital accountability to the thermodynamic limits of solar energy conversion. Using real-time meteorological data, geospatial coordinates, and first-principles calculations of solar yield, the system establishes a hard physical boundary for every panel's maximum possible output; any reported generation exceeding this limit is automatically rejected before entering the shared ledger. This trustless verification enables a peer-to-peer marketplace with programmatic reward structures that continuously reinvest value into equipment maintenance and market liquidity, preventing the speculative hoarding that typically destabilizes blockchain-based marketplaces. When electricity is consumed, the corresponding digital credits are permanently retired in direct proportion to physical energy dissipation, creating an auditable one-to-one mapping between urban consumption and carbon accounting. Deployed across heterogeneous city nodes, the prototype demonstrates resilience against data injection attacks while lowering capital barriers for community-level solar expansion. Beyond energy, the framework offers a general model for coordinating economic activity with physical law in any domain where distributed infrastructure demands both data integrity and sustainable investment. We release the data and code as open-access on GitHub.

This paper examines how estimates of AI use in scientific writing can be biased when evaluation methods ignore contextual differences across countries and fields. Using large-scale data on journal publications from Dimensions, we construct AI-likeness benchmarks based on differences between human-written and LLM-rephrased abstracts. We show that a pooled benchmark may confound pre-existing stylistic variation with AI-generated text, producing substantial distortions across country-field groups even in pre-LLM publications. In contrast, country-field-specific benchmarks attenuate such distortions and provide a more credible baseline for comparison. Applying these methods to publications in 2025 reveals that the pooled benchmark systematically overestimates AI use in certain countries and fields while underestimating it in others. These findings highlight the importance of context-aware measurement for accurate and equitable evaluation of AI use in science.

Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes and Heston models. The framework takes classical contract and model data as input and returns classical estimates of selected option values. We solve the pricing PDEs after finite-difference discretization on spatial grids. For $N=2^n$ grid points per spatial direction and $d$ assets, the end-to-end gate complexity for single-point recovery, counted in elementary CNOT gates and one-qubit Pauli-axis rotations, has leading grid-size dependence $\widetilde{O}(d^2 N^{2+d/2})$ for local-volatility Black--Scholes and $\widetilde{O}(d^2 N^{d+2})$ for Heston. Relative to grid-based finite-difference baselines, these scalings correspond to polynomial improvement factors $N^{d/2}$ and $N^d$, respectively. These estimates translate to Clifford+T resources via standard compilation. We complement the complexity analysis with numerical benchmarks against standard classical methods. In the Heston setting, the framework recovers option prices across strikes together with the associated implied-volatility smile/skew. Overall, this work provides a complete end-to-end quantum pricing pipeline with explicit resource accounting and theoretical performance guarantees.

We propose a foundational runtime actuarial layer for autonomous AI agents in which every side-effect-bearing action carries a time-consistent, counterfactual risk toll computed against a contractually fixed safe default, inside an explicit underwriting boundary. The framework treats per-action insurance as the primary unit of analysis and replaces post-hoc annual liability cover with a pre-action transaction layer. The paper establishes four structural results: (i) a well-defined counterfactual toll under a chosen safe-default mapping and continuation policy, with explicit non-uniqueness; (ii) a no-splitting property within an underwriting boundary that telescopes path-decomposed actions into a boundary potential, with a corollary tying gaming-resistance to boundary design; (iii) an irreversible-authority premium, split into a strictly positive action-level component and an if-and-only-if characterisation of the set-level robust capital increase; and (iv) a conservative runtime gating theorem that translates high-probability toll envelopes into an executed-action budget guarantee. The result is the mathematical base layer for a broader program: an empirical companion instantiates the runtime through an Actuarial Action Interface and authority-frontier experiments; a mechanism-design companion studies strategic operator incentives and cross-boundary aggregation; and a dynamic-underwriting companion studies experience rating and audit-replay calibration. The present paper states the primitive contract, the toll identity, the within-boundary no-arbitrage result, and the budget guarantee on which those later layers depend.

Researchers have started using LLM agents in place of human subjects in behavioural and political-science experiments, often as a cheaper substitute for laboratory pools. The substitution does not hold up in strategic settings: humans and LLMs reliably make different choices, and neither fine-tuning on human response data nor persona conditioning has closed the gap. The behavioural-economics literature has, since Simon's introduction of bounded rationality, modelled human strategic behaviour as a classical baseline plus an additive correction term $δ$. The framework proposed here reads $δ$ as the mathematical signature of bounded computation: the gap between what an unboundedly-rational agent would compute and what a computationally bounded agent actually produces. For canonical games whose solutions are present in standard training corpora, LLMs retrieve and recombine corpus material, bypassing the bound that produces $δ$ in humans. The framing extends to reasoning-distilled models through cognitive-hierarchy theory: their accessible level-$k$ strategic reasoning is bounded by compute budget and context length rather than by the cognitive constraints that bound humans, and the $δ$ they produce, if any, carries different structural signatures. Four operational tests (conditional dependence, distributional asymmetry, path-dependence under repetition, and paraphrase-robustness) are proposed to discriminate human-shaped $δ$ from LLM-shaped $δ$. A moderator prediction is that $|δ|$ scales with peer-signal individuation in the decision environment, with a quantitative bound of Cohen's $d \geq 0.5$ between named-opponent and aggregate-opponent settings.

In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional Itô formula developed by [Viens, F., & Zhang, J. (2019). A martingale approach for fractional Brownian motions and related path dependent PDEs. Ann. Appl. Probab.]. We then leverage these tools to study weak rates of convergence for discretised stochastic integrals of smooth functions of a Riemann-Liouville fractional Brownian motion with Hurst parameter $H \in (0,\frac{1}{2})$. These integrals approximate log-stock prices in rough volatility models. We obtain the optimal weak error rates of order $1$ if the test function is quadratic and of order $(3H+\frac{1}{2})\wedge1$ if the test function is five times differentiable; in particular these conditions are independent of the value of $H$.

Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks (GAT) to capture evolving inter-stock relationships, and sentiment analysis of financial news to reflect market psychology. Unlike prior approaches, our model unifies these elements in a single pipeline that produces daily allocations. It avoids the traditional two-step process of forecasting asset returns and then applying mean--variance optimization (MVO), a sequence that can introduce instability. We evaluate the framework on nine U.S. stocks spanning six sectors, chosen to balance sector diversity and news coverage. In this setting, the model delivers higher cumulative returns and Sharpe ratios than equal-weighted and CAPM-based MVO benchmarks. Although the stock universe is limited, the results underscore the value of integrating price, relational, and sentiment signals for portfolio management and suggest promising directions for scaling the approach to larger, more diverse asset sets.

We study the problem of hedging unit linked life insurance policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges: constructing a green investment fund and developing a hedging strategy for policies written on that fund. We address these two problems separately. First, we design a portfolio selection rule driven by firms' carbon intensity that endogenously selects assets and avoids ad hoc pre-screens based on ESG scores. The effectiveness of our new portfolio selection method is tested using real market data. Second, we consider an insurance company issuing unit linked policies written on this fund. Such contracts are exposed to market, carbon, and mortality risk, which the insurance company seeks to hedge. Due to market incompleteness, we address the hedging problem via a quadratic approach aimed at minimizing the variance of the hedging costs. Finally, we also make a numerical analysis to assess the performance of the hedging strategy. For our simulation study, we use an efficient weak second-order scheme that allows for variance reduction.

We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.

Mandatory waiting periods have been instituted for medical procedures, gun purchases, and other high-stakes decisions. Are these softly paternalistic policies substitutes for harder restrictions, and are delayed decisions more respected? In a general population survey experiment, Choice Architects make rules for decision-makers facing a high-stakes Bomb Risk Elicitation Task. Treatments vary when the decision is made: on the spot or after one day, and whether the initial decision can be revised. Choice Architects set a cap on the decision-maker's risk taking; in one treatment, they can additionally implement a mandatory waiting period. Exogenous deliberation has no effect on the cap; equivalence testing (TOST) and Bayesian analysis ($\text{BF}_{01} \approx 12$) provide strong positive evidence for the absence of an effect. Endogenously prescribed waiting periods are add-on restrictions that do not substitute for the cap. Choice Architects believe that, with time, the average decision-maker will take less risk and -- because of the distribution of Choice Architects' bliss points -- come closer to Choice Architects' subjective ideal choice; the resulting reduction in forecasted errors is small. Soft and hard paternalistic instruments are not substitutes: waiting periods are deployed as add-on restrictions.

How informative are job ads about the actual pay and non-pay attributes offered by employers? Using a comprehensive database of job ads posted by Norwegian employers, we develop a methodology to systematically classify the pay and non-pay job attributes advertised in vacancy texts. About 60% of job ads provide pay-related information and nearly all ads feature information on non-pay attributes. We link these advertised attributes to the employers posting the ads and validate this information against revealed-preference measures of employer quality, realized attributes, and choices from a survey experiment. All three strategies confirm that job ads provide reliable signals of employer quality. We then incorporate the detailed job attributes in a monopsony framework and quantify their contribution to labor market inequality.

An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders' belief and risk aversion. This paper proposes a trading strategy model in the optimal Merton framework that is representative of the collective behavior of heterogeneous rational traders. This model allows for the estimation of the average risk aversion of traders acting on a specific risky asset, while revealing the existence of a price of risk closely related to market price of risk and volume rate. The empirical analysis, conducted on real data, confirms the validity of the proposed model.