The composite likelihood method reduces the computational cost of parameter estimation in time series by considering several subsets of observations instead of all observations at once. The asymptotic properties of this method are related to the Godambe information, an extension of the Fisher information that accounts for the dependence between subsets of observations. We aim to apply this method to linear Gaussian models, in particular fractional Brownian motion and fractional Gaussian noise. We derive theoretical expressions for their Fisher information and their Godambe information and deduce a subset selection design that sequentially maximizes the Godambe information. The size of the subsets then allows us to control the trade-off between estimation accuracy and computational cost. Through simulations, we compare this method with the method of moments and maximum likelihood estimation, and we apply it to real data, namely volatility series of a stock index and a wind speed time series.

Generating stochastic trajectories for asset classes is an increasingly relevant task in quantitative finance. Traditional approaches, such as the stationary bootstrap, preserve by construction the empirical distribution of asset-class returns, but do not ensure that each individual simulated path is economically realistic: scenarios may be valid in distribution while single trajectories fail to represent plausible states of the world. To address this limitation, we review semiparametric simulation methodologies that combine a parametric structure, which enforces realistic dynamics, with the resampling of model residuals, which preserves the stochastic component observed in historical data. The issue is particularly acute for interest rates, where direct resampling of rate changes may produce implausible yield-curve evolutions despite correct distributional properties. Our empirical analysis shows the effectiveness of semiparametric bootstrap methods based on autoregressive or mean-reverting specifications. In the fixed-income setting, combining these methods with fully parametric term-structure models yields more coherent and realistic simulations of yield-curve dynamics.

In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.

We consider a continuous time investment problem in a multi-asset Black-Scholes market with the following features: The assets' drifts are not known and constitute a source of model ambiguity. However, there is a prior distribution (knowledge) on the possible drifts. Our investor is ambiguity averse and wants to maximize a mean-variance criterion for the terminal wealth where ambiguity aversion is incorporated in a smooth way. We consider here the criterion introduced in Maccheroni et al. 2013 where the variance is decomposed and each part is weighted differently to account for different levels of market risk and model ambiguity aversion. We use a novel approach to find the optimal dynamic investment strategy within the class of all adapted strategies which allow for learning. We also present a number of numerical results which help to understand how the model parameters affect the optimal investment strategy. In general it turns out that ambiguity averse investors invest less in the risky assets.

Ship finance is a data-intensive and document-heavy segment of asset-based lending, requiring the integration of financial, technical, contractual, and regulatory information from heterogeneous and largely unstructured sources. Increasing environmental regulation and ESG reporting requirements are adding further complexity to underwriting and loan-origination processes. Recent advances in artificial intelligence (AI), particularly large language models (LLMs), create new opportunities for processing and analysing such information. This paper reviews potential applications of AI in ship finance, with a particular focus on LLM-based systems for document comprehension, information extraction, and workflow automation. We present this http URL, a modular agentic architecture to support loan application workflows in ship finance. The proposed system combines an LLM-based extraction module, financial analysis components, external maritime data services, and a controlled document-generation module with a chatbot interface to support the preparation of standardized financing applications. The paper discusses the key challenges for using such models in production. We argue that AI-assisted systems can support maritime finance professionals in managing increasingly complex information and reporting requirements.

We study Bermudan option pricing under the Gatheral Double Mean-Reverting (GDMR) stochastic volatility model. The model features a variance process together with a stochastic long-run mean variance process and allows Constant Elasticity of Variance (CEV)-type exponents in the diffusion coefficients. This model is attractive since it provides a flexible specification for volatility dynamics. However, the pricing of early-exercise derivatives under the GDMR model remains largely unexplored in the literature. To address this challenge, we adapt a Hybrid Least-Squares Monte Carlo-Partial Differential Equation (LSMC-PDE) framework to the GDMR model and provide a detailed model-specific implementation. Conditioning on simulated variance paths, the pricing problem reduces to a one-dimensional problem in the asset price, which is solved by a Fourier-based approach, while the remaining dependence on the variance variables is approximated by least-squares regression. Our numerical experiments demonstrate that the Hybrid LSMC-PDE approach yields accurate pricing estimates and often lower pricing errors than plain LSMC, particularly for low and moderate numbers of simulation paths, showing the benefit of using the model structure in early-exercise option pricing.

Quantifying worst-case and best-case performance under complex market scenarios is a persistent challenge in financial risk management and the verification of path-dependent financial instruments, such as exotic options and structured products. Simulation-based methods are well suited for probabilistic estimation, but they do not directly provide exhaustive guarantees over all admissible scenarios or explicit witnesses for extremal outcomes. To address this, we introduce a quantitative automata-based framework for the exact extremal analysis of financial systems under declarative scenario constraints. At the core of our approach are event history automata (EHAs), a new formal model that integrates regular-expression event patterns with admissible numerical intervals to represent constrained event histories with memory. Quantitative payoffs are represented by weighted finance finite automata (WFFAs), which allow transition weights to depend on observed market values. By computing the synchronized product of EHAs and WFFAs, our framework enables the exact calculation of upper and lower payoff bounds. Furthermore, the method automatically extracts interpretable witness event histories that realize these extremal outcomes. We demonstrate the practical viability of the approach through a case study of an autocallable structured product with path-dependent mechanisms. The case study analyzes how different scenario constraints affect coupon accumulation, early redemption, and protection-loss outcomes. Scalability experiments indicate that the framework's execution remains computationally feasible for practical contract horizons and nontrivial constraint configurations. Overall, this approach provides a mathematically rigorous complement to standard financial simulation methods.

We consider the problem of estimating the true Sharpe ratio of an asset selected for having the highest observed in-sample Sharpe ratio among many assets. We discuss estimators based on the polyhedral lemma, James Stein shrinkage, debiasing the expected maximum Sharpe ratio, thresholding and empirical Bayes. We test these estimators in simulations, computing bias and root mean square error across different values of sample size, number of assets, and spread and shape of population Sharpe ratios. We also compute rank correlation of the estimators against the underlying quantity, simulating how these estimators might be used to compare or rank the output of different teams which perform this selection process. We find that the James Stein estimator provides the best performance across many different realistic values of the relevant parameters, followed by the GMLEB estimator of Jiang and Zhang. These results are fairly robust to correlation of asset returns, with some caveats.

We present two explicit rational formulae for Bachelier, or normal, implied volatility. The formulae take the option price, forward, strike, and expiry as inputs and return the implied normal volatility without iteration. They follow the branch structure of LFK-4, but use the simpler near-the-money variable given by the absolute forward-strike difference divided by the tail time value, avoiding a logarithm and a small-argument Taylor branch in that region. LFK-2026 is the accuracy-oriented formula and approximates reciprocal absolute standardized moneyness directly in the far tail. LFK-2026C keeps the same shifted out-of-the-money rational tail approximation, but splits the near-the-money branch two low degree rationals. In double precision tests both remain close to machine accuracy, while LFK-2026C is the faster scalar implementation on the current benchmark mix.

The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on average. For some size-based stock portfolios, dividing their returns by the Volatility Index makes them closer to independent and normal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, relative size, and CAPM. We fit this model using real-world data, prove the long-term stability, and connect this research to Stochastic Portfolio Theory. We fill important gaps in our previous article on CAPM with the size factor.

Real-world financial decision-making is a challenging problem that requires reasoning over heterogeneous signals, including company fundamentals derived from regulatory filings and trading signals computed from price dynamics. Recently, with advances in Large Language Models (LLMs), financial analysts have begun to use them for financial decision-making tasks. However, existing financial question-answering benchmarks for testing these models primarily focus on company balance sheet data and rarely evaluate reasoning about how company stocks trade in the market or their interactions with fundamentals. To leverage the strengths of both approaches, we introduce FinTradeBench, a benchmark for evaluating financial reasoning that integrates company fundamentals and trading signals. FinTradeBench contains 1,400 questions grounded in NASDAQ-100 companies over a ten-year historical window. The benchmark is organized into three reasoning categories: fundamentals-focused, trading-signal-focused, and hybrid questions requiring cross-signal reasoning. To ensure reliability at scale, we adopt a calibration-then-scaling framework that combines expert seed questions, multi-model response generation, intra-model self-filtering, numerical auditing, and human-LLM judge alignment. We evaluate 14 LLMs under zero-shot prompting and retrieval-augmented settings and witness a clear performance gap. Retrieval substantially improves reasoning over textual fundamentals, but provides limited benefit for trading-signal reasoning. These findings highlight fundamental challenges in the numerical and time-series reasoning for current LLMs and motivate future research in financial intelligence.

We describe a post hoc test for the Sharpe ratio, analogous to Tukey's test for pairwise equality of means. The test can be applied after rejection of the hypothesis that all population Signal-Noise ratios are equal. The test is applicable under a simple correlation structure among asset returns. Simulations indicate the test maintains nominal type I rate under a wide range of conditions and is moderately powerful under reasonable alternatives.

We propose a stochastic game modelling the strategic interaction between market makers and traders. From the trader's perspective, the conventional exogenous permanent price impact is replaced by the endogenous quoting strategies of the market makers. Conversely, from the market maker's perspective, order flows are no longer assumed to be exogenous, but are driven endogenously by the strategic traders. Characterizing the Nash equilibria via forward-backward stochastic differential equations (FBSDEs), we establish a local well-posedness result for the general game. For the specific `Almgren-Chriss-Avellaneda-Stoikov' model, the decoupling approach guarantees the global well-posedness of the FBSDEs by reducing it to a backward stochastic Riccati equation with $M_+$-matrix coefficients. Finally, by introducing small diffusion terms into the inventory processes as an approximation to the general game, we establish its global well-posedness. Simulations reveal a negative correlation between quotes and strategic orders, in contrast to the positive correlation observed between quotes and noise orders.

This paper studies a type of periodic utility maximization problem for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon, featuring the dynamic adjustments in portfolio decision according to past achievements. Under power utility, we transform the original infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem under a modified utility function. To cope with the convex trading constraints, we further introduce an auxiliary unconstrained optimization problem in a modified market model and develop the martingale duality approach to establish the existence of the dual minimizer such that the optimal unconstrained wealth process can be obtained using the dual representation. With the help of the duality results in the auxiliary problems, the relationship between the constrained and unconstrained models as well as some fixed point arguments, we derive and verify the optimal constrained portfolio process for the original problem over an infinite horizon.

Introduction. The high prevalence of students not achieving basic learning competencies in Latin America (LAC) is concerning, even more so considering the region's deep structural inequalities and the larger post-pandemic learning losses. Within this scenario, the paper aims to contribute to the identification of the determinants of bottom and low performers (below level 2). Methodology. Based on 2022 data from the Programme for International Student Assessment (PISA) for 10 LAC countries, and using a stacking model integrating binary classification models as well as by applying Shapley Additive Explanations (SHAP) analysis for interpretability, we identify critical factors impacting on the student performance across low performers groups. Results. We find that a student with the highest probability of being a not achiever speaks a minority language and had repeated, has no digital devices at home, comes from a poor family and works for payment half of the week, and the school the student attends has wide disadvantages such as bad school climate, weak Information and Communication Technology (ICT) infrastructure and poor teaching quality (only a third of teachers being certified). For countries' estimates, we find quite homogeneous patterns regarding the contribution of top ranked factors, with repetition at primary, household wealth, and educational ICT inputs being top ten ranked covariates in at least 8 out of the 10 total countries. Discussions. The paper findings contribute to the broad literature on strategies to identify and to target those most left behind in Latin American education systems.

Latin America's education systems are fragmented and segregated, with substantial differences by school type. The concept of school efficiency (the ability of school to produce the maximum level of outputs given available resources) is policy relevant due to scarcity of resources in the region. Knowing whether private and public schools are making an efficient use of resources --and which are the leading drivers of efficiency-- is critical, even more so after the learning crisis brought by the COVID-19 pandemic. In this paper, relying on data of 2,034 schools and nine Latin American countries from PISA 2022, I offer new evidence on school efficiency (both on cognitive and non-cognitive dimensions) using Data Envelopment Analysis (DEA) by school type and, then, I estimate efficiency leading determinants through interpretable machine learning methods (IML). This hybrid DEA-IML approach allows to accommodate the issue of big data (jointly assessing several determinants of school efficiency). I find a cognitive efficiency gap of nearly 0.10 favouring private schools and of 0.045 for non-cognitive outcomes, and with a lower heterogeneity in private than public schools. For cognitive efficiency, leading determinants for the chance of a private school of being highly efficient are higher stock of books and PCs at home, lack of engagement in paid work and school's high autonomy; whereas low-efficient public schools are shaped by poor school climate, large rates of repetition, truancy and intensity of paid work, few books at home and increasing barriers for homework during the pandemic.

Several key states in various regions of the U.S. have experienced recent sawtimber as well as pulp and paper mill closures, which raises an important policy question: how have and will key macroeconomic and industry specific indicators within the U.S. forest sector likely to change over time? This study provides empirical evidence to support forest-sector policy design by using a vector error correction (VEC) model to forecast economic trends in three major industries - forestry and logging, wood manufacturing, and paper manufacturing - across six of the most forest-dependent states found by the location quotient (LQ) measure: Alabama, Arkansas, Maine, Mississippi, Oregon, and Wisconsin. Overall, the results suggest a general decline in employment and the number of firms in the forestry and logging industry as well as the paper manufacturing industry, while wood manufacturing is projected to see modest employment gains. These results also offer key insights for regional policymakers, industry leaders, and local economic development officials: communities dependent on timber-based manufacturing may be more resilient than other forestry-based industries in the face of economic disruptions. Our findings can help prioritize targeted policy interventions and inform regional economic resilience strategies. We show distinct differences across forest-dependent industries and/or state sectors and geographies, highlighting that policies may have to be specific to each sector and/or geographical area. Finally, our VEC modeling framework is adaptable to other resource-dependent industries that serve as regional economic pillars such as mining, agriculture, and energy production offering a transferable tool for policy analysis in regions with similar economic structures.