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on Risk Management |
| By: | Nawaf Mohammed; Edward Furman |
| Abstract: | We compare two natural proportional notions of a risk component's contribution to the aggregate tail risk of a collection of risks: the fraction of aggregate tail risk capital allocated to the component under Conditional Tail Expectation (CTE), and the component's expected realized share of aggregate risk under Geometric Tail Expectation (GTE). The resulting proportional allocations generally differ. For arbitrary random vectors-allowing atoms, signed risks, and any tail domain--we establish when the allocations agree, determine their ordering when they do not, and characterize their asymptotic separation. Both proportional allocations are weighted averages of the conditional risk share of a component given the aggregate: the proportional CTE allocation weights tail scenarios by severity, whereas the proportional GTE allocation weights them uniformly. Their difference is therefore a normalized tail covariance. The proportional CTE and GTE allocations agree throughout a tail exactly when the conditional risk share is constant there; under a mild unimodality condition, dominance is characterized by its monotonicity. Among independent exponential dispersion models with heterogeneous natural parameters, exact agreement is possible only for the scaled Poisson family; under comonotonicity, it is equivalent to proportional quantile functions. In the extreme tail, the limiting relationship between the proportional CTE and GTE allocations is governed by the ratio of Expected Shortfall to Value-at-Risk: boundedness ensures common limits, convergence to one forces the allocations to merge, and divergence can cause their limits to separate. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.36177 |
| By: | Matteo Crosignani; Lina Han; Marco Macchiavelli |
| Abstract: | Geoeconomic risk—the risk that firms incur valuation losses when countries deploy economic, trade, or financial leverage for geopolitical aims—has become a first-order concern for investors. In this post, based on our recent Staff Report, we document that domestic U.S. stocks expose investors to substantial geoeconomic risk through firms’ global supply-chain relationships, affecting investors’ returns and portfolio allocation. We also find that investors are compensated for bearing geoeconomic risk through higher risk premia. |
| Keywords: | mutual funds; Asset allocation; geoeconomic risk; export controls |
| JEL: | G12 F51 F38 |
| Date: | 2026–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednls:103863 |
| By: | Hyeyoon Jung; Jaehoon (Kyle) Jung |
| Abstract: | In an April post, using millions of homeowners’ insurance contracts matched with property-level exposure and disaster risk, we showed that although households are insured, they are still “on the hook” because deductibles and coverage limits leave homeowners responsible for part of a loss. Because insurers cannot perfectly observe how well homeowners maintain or protect their properties (a problem known as “moral hazard”), contract terms such as deductibles can play an important role in balancing risk sharing and incentives. By requiring homeowners to bear part of a loss, insurers can preserve incentives for policyholders to take actions that reduce damage risk. In this post, we quantify the cost of keeping homeowners on the hook. How costly is moral hazard in homeowner’s insurance? How much risk must households retain to preserve these incentives? And, importantly, who ultimately bears that residual risk? The short answer is that keeping homeowners on the hook costs insurers relatively little, but it leaves households with substantial risk, especially those least able to absorb a large loss. |
| Keywords: | insurance; financial constraints; household finance; moral hazard; contracting |
| JEL: | C6 D8 G1 G2 G3 |
| Date: | 2026–10–05 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednls:103873 |
| By: | Ryan M. Engel; Kibaek Lee; Namid Stillman |
| Abstract: | Financial returns are heavy-tailed, and accurate tail risk estimation is central to portfolio risk management. Modern neural generators sample by pushing a simple base distribution through a learned map, and for training stability that map is built from Lipschitz components. This is the binding constraint: a Lipschitz map of a Gaussian is sub-Gaussian, so heavier-tailed targets admit no exact match at any finite Lipschitz constant. The Monge--Amp\`ere equation ties the Brenier map's local distortion to the density ratio $f/(g\circ T)$, so a deeper trough in the target density requires a higher-gain map and yields a higher-variance estimator. The argument needs only bounded distortion, so it covers normalizing flows, flow matching, GANs, and diffusion samplers alike. Semi-Discrete Optimal Transport (SDOT) relaxes the map's regularity rather than the source's tail class. Its power diagram gives every training observation a cell holding exactly $1/N$ of the source measure, and tail observations are reached by crossing a cell boundary rather than by stretching. Our primary experiment sweeps severity over a calibrated Merton jump-diffusion spanning kurtosis 94 to 1, 679. SDOT holds tail ratios at $0.85$--$0.94$ with cross-seed standard deviations below $0.025$, while every learned generator either compresses the tails or inflates them with a variance that grows alongside. Further experiments carry the result to real S\&P~500 returns and to a 21-year backtest, where SDOT gives the best risk-adjusted market-neutral strategy under CVaR optimization (Sharpe $0.70$, max drawdown $-2.60\%$, against $0.40$ for the next-best generator). |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.27785 |
| By: | Wee Ling Tan; Stephen Roberts; Stefan Zohren |
| Abstract: | We present an end-to-end deep learning framework for systematic options trading that directly embeds hedging behavior through explicit control of portfolio-level risk exposures. While neural networks trained to optimize risk-adjusted performance have been shown to outperform traditional rules-based strategies, such approaches remain agnostic to the sensitivities of the resulting portfolios with respect to specific underlying risk factors. We propose a general training objective that combines a performance-driven loss with a differentiable risk-sensitivity penalty, enforcing neutrality to selected risk dimensions. Unlike reinforcement learning methods that approximate optimal hedging policies via simulated market dynamics, our framework operates entirely on historical data and jointly optimizes risk-adjusted returns and targeted risk constraints in a single learning problem. We instantiate the framework on static delta-neutral straddle portfolios with the penalty directed at first-order directional exposure, and evaluate two penalty variants -- an exposure-normalized penalty and a Greek-ratio drift penalty. Empirical results on Nasdaq 100 equity options demonstrate that appropriately calibrated regularization simultaneously improves out-of-sample risk-adjusted performance relative to an unregularized baseline while reducing realized directional exposure. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.33767 |
| By: | Jonas Brunholm; Bjarne H{\o}jgaard; Thomas D. Nielsen; Orimar Sauri |
| Abstract: | This paper proposes a framework for modeling probability of default via functional data analysis. By representing a series of credit variables as functions, we investigate whether intra-monthly information improves default predictability in linear models. We further show how a range of widely used variables, among them available funds, utilization rate, and overdraft, can all be derived from three quantities observed over time. Namely, 1) the type of each account, 2) the balance of the account, and 3) the size of the credit limit on the account. Retaining these quantities as continuous-time processes, rather than reducing them to monthly aggregated values, yields a continuous faithful representation of the borrower. When analyzing these three processes, we discovered that recurring events associated with the ordinal position among banking days created strong cyclical patterns. We therefore develop a relative time framework that aligns the recurring events across borrowers, ensuring that borrowers possess the same cyclical pattern, regardless of real time. We assess the framework using functional logistic regression. This approach accommodates the continuous representation while remaining closely related to a logistic regression model commonly used in credit risk practice, due to strict regulatory constraints. We show that, when equipped with an effective functional representation of transactional trajectories, the proposed model attains predictive performance on par with XGBoost while consistently outperforming logistic regression. Importantly, the model balances predictive performance of a machine learning model with the interpretability of linear default models, potentially enabling financial institutions to use the model, even under strict regulation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.07888 |
| By: | Jean-Loup Dupret; Donatien Hainaut; Edouard Motte |
| Abstract: | We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. The hedging functional is restricted to a reproducing kernel Hilbert space whose kernel is parameterized through a neural network embedding of the input features. The framework minimizes a regularized empirical risk under convex loss functions and can accommodate path-dependent information through truncated time-augmented signature features. We derive a generalized representer theorem for the joint hedging problem, reducing the empirical optimization to a finite-dimensional problem. To further reduce the computational cost associated with large kernel matrices, we develop a scalable random Fourier feature approximation and establish convergence guarantees. The random Fourier parameters are sampled once and remain fixed throughout training, while the deep kernel adapts to market data through the learned neural representation. We evaluate the performance of the proposed deep kernel approach on both synthetic and real data and compare it with standard kernel methods and classical deep hedging architectures. Numerical results indicate competitive and robust hedging performance, particularly in low-data regimes, which highlights the benefits of combining expressive neural representations with the inductive bias of kernel methods. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.34474 |
| By: | Thomas Schmelzer |
| Abstract: | In a recent paper, Schmelzer and Hastie argue that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. Here we use that identity to compute efficient frontiers with a stock LASSO solver, \texttt{lars\_path} from \texttt{scikit-learn}. It handles long--short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Called naively, the last path stops at the maximum-Sharpe portfolio. One shift of the response, by an amount computed in advance, lets a single call reach the minimum-variance portfolio. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.37108 |
| By: | Wenyuan Wang; Zuo Quan Xu; Kaixin Yan |
| Abstract: | We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic control problem, and we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with nonlocal operator. For almost all parameter configurations, we explicitly characterize the optimal strategy that maximizes the expected total discounted dividends net of transaction costs until ruin. The optimal dividend policy is a two-barrier impulsive strategy, while the optimal reinsurance proportion is given in feedback form. Numerical examples are provided to illustrate the optimality results. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.32686 |
| By: | Sha\"in Afzali; Serena Della Corte; Antonis Papapantoleon |
| Abstract: | Neural network-based approaches have emerged as efficient alternatives to traditional optimization-based procedures for the calibration of stochastic volatility models. However, existing work has focused primarily on predictive accuracy, with comparatively little attention devoted to understanding the structure of the learned inverse calibration mappings. In this work, we analyze neural calibration mappings for the Heston and rough Heston models across multilayer perceptron, highway, and softmax-parametrized highway architectures, using complementary Shapley-based methods from explainable AI. Specifically, we consider SHAP and $\nu$SHAP explanations, which capture distinct, complementary notions of feature relevance, corresponding to sensitivity and sufficiency of feature subsets, respectively. Short maturities and smile wings consistently dominate parameter inference, and the dominant attribution structure remains qualitatively stable across architectures despite differences in predictive accuracy and parameter count. Parameter-specific differences between SHAP and $\nu$SHAP further reveal how distinct regions of the implied volatility surface contribute to parameter recovery and expose substantial redundancy in the calibration input. Building on this redundancy, we show that $\nu$SHAP explanations can guide a significant reduction in input dimensionality for the rough Heston model while matching calibration accuracy relative to the full implied volatility surface. These findings demonstrate that complementary Shapley-based methods provide structural insight into learned inverse calibration mappings beyond predictive error metrics, and offer a practical route to feature selection in neural calibration problems. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.03076 |
| By: | Masahiro Kato |
| Abstract: | This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.02290 |
| By: | Fr\'ed\'eric Pauquay |
| Abstract: | We develop a non-perturbative framework for stochastic-volatility option pricing organised by the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables is approximated by a self-consistent Gaussian whose mean and effective diffusion follow from the 2PI stationarity conditions, with the drift Jacobian given by statistical linearisation. The smile-generating exponential and CEV interactions are evaluated through the exact Gaussian moment-generating function rather than a Taylor cut. Whether the dressed inverse propagator is local in time separates Markovian models, where the gap equation collapses to a few ODEs, from rough (Volterra) models, where the full two-time propagator is retained and the characteristic function becomes a Gaussian integral over the log-variance field. Across exp-OU, SABR, rough Bergomi and rough SABR, the resulting deterministic engines match PDE or quasi-Monte-Carlo references from sub-basis-point (exp-OU) through single-digit basis points (SABR, rough Bergomi) to tens of basis points (rough SABR), with rough Heston as an exactly-transformable control. Conditional on the volatility field, forward-start smiles and continuously-monitored barriers reduce to field-only quadratures, in rough Bergomi directly on the native Volterra field, and the causal response block yields the full impulse-vega curve in one contraction at one-to-two orders of magnitude below bump-and-revalue. A technical supplement with complete derivations, extended benchmarks and secondary applications (stochastic-rate FX local volatility, quadratic Gaussian Volterra variance and the arbitrage-free FX triangle) is provided as an ancillary file. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.37741 |
| By: | Alexander Ardaiz; Varun Budati; Ali Habibnia |
| Abstract: | Deep reinforcement-learning policies for order execution can vary substantially across training seeds, so apparent architectural gains may reflect favourable training realisations rather than reproducible properties of the architecture. We evaluate vanilla Double Deep Q-Learning (DDQL), K-means-partitioned mixtures of DDQL experts at $K \in \{2, 4, 8\}$, and dense networks parameter-matched to the $K{=}4$ and $K{=}8$ expert budgets on 5-minute mean-aggregated BTC/USDT limit order book data from Binance. No learned configuration significantly improves mean implementation shortfall over DDQL. Under the reported specification, all have higher mean shortfall than TWAP (0.39 bps) and immediate liquidation (0.21 bps) in an environment whose frictionless replay and terminal-urgency penalty make early liquidation nearly costless; 11/100 vanilla-DDQL runs, versus none in either MoE $K{\geq}4$ arm, converge to a policy that waits until forced liquidation. We then decompose this specification on a device-matched baseline. Annealed exploration alone eliminates observed collapses (12/100 to 0/100; exact McNemar $p{=}4.9{\times}10^{-4}$), matching the elimination under expert partitioning. Combining annealed exploration with the aligned reward restores collapse in 19/30 runs; with all three specification changes, it rises to 48/100. In this environment, expert partitioning is unnecessary to suppress collapse and appears to mask a training-specification failure rather than confer an intrinsic performance benefit. No MoE $K{=}8$ run collapses under any of the six specifications tested. Across-seed dispersion is lowest at $K{=}8$ but non-monotone and not robust to family-wise adjustment, while within-policy tail risk worsens monotonically with $K$. The apparent attribution of the failure mode reverses between 30 and 100 seeds, illustrating the importance of repeated-seed evaluation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.03369 |
| By: | Ingrid Ott; Susanne Soretz |
| Abstract: | Rapid technological change can generate risks that extend beyond the actors creating them, while institutional capacity to contain these risks adjusts only gradually. Strategic rivalry can reinforce this mismatch by sustaining incentives for technological acceleration even as risk increases. The interaction of endogenous risk creation with institutional inertia can therefore transform a quantitative imbalance between risk creation and governance-capacity formation into a qualitative viability problem: beyond a critical boundary, a low-risk equilibrium ceases to exist. We develop a differential game in which countries choose technological acceleration and governance mobilization. These flows accumulate into technological capability, a common risk stock, and effective governance capacity. Technological capability has productive and strategic value, whereas aggregate acceleration generates risk that is only partially internalized. Rising risk strengthens incentives for containment but can simultaneously increase the strategic value of relative technological capability. Governance mobilization responds to risk but becomes effective only as it is gradually converted into governance capacity. Relative to a multilateral cooperative benchmark, the non-cooperative equilibrium features excessive technological acceleration and insufficient governance mobilization. We map these equilibrium responses into a two-dimensional risk--governance system, which yields an endogenous viability frontier. "Low-risk'' denotes an equilibrium in which accumulated governance capacity is sufficient to balance endogenous risk creation; it does not imply intrinsically low or socially optimal risk. Institutional delay can therefore shift the policy problem from correcting an externality toward preserving a dynamically sustainable balance between risk creation and governance capacity. We apply the framework to current AI policy configurations and AI-enabled synthetic biology. Rapid and increasingly distributed technological capability raises informational, monitoring, and coordination requirements for effective safeguards and can narrow the margin within which risk creation remains dynamically containable. |
| Keywords: | dynamic risk externalities, institutional inertia, nonlinear dynamics, viability frontier, strategic technological competition, artificial intelligence |
| JEL: | D62 O33 H41 C73 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13024 |
| By: | Kelvin J. L. Koa; Filip Orestav; Shengqiong Wu; Michael J. Wooldridge; Ke-Wei Huang |
| Abstract: | While symbolic regression (SR) has been successfully used in science to discover new equations, its use in financial valuation is hindered by several limitations. Whereas the natural sciences provide objectively correct relationships, financial valuation constitutes a distinct class of symbolic discovery problems, as it admits multiple valid perspectives, operates under non-stationary market conditions, and involves noisy, continuous performance signals. In this work, we propose Multi-Agent Fundamental Analysis with Symbolic Adaptive learning (MUFASA), a hierarchical multi-agent framework for symbolic discovery in finance. MUFASA introduces (1) disentangled equation discovery via specialized agents representing distinct valuation perspectives, (2) a meta-coordinator that performs hierarchical-level reasoning over market context information, and (3) a memory mechanism that reasons over statistical performance summaries (e.g., accuracy, stability, and tail risk) to guide learning under noisy feedback. Experiments across datasets from multiple countries show that MUFASA achieves state-of-the-art performance on the valuation task compared to classical finance methods, financial large language models, and SR approaches, while simultaneously producing interpretable equations, which we share with the community. We also make publicly available the distilled learnings across evolution iterations and context-dependent strategy weights, which might offer useful insights for future research on financial fundamental analysis. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.32746 |
| By: | Arthur Charpentier (UQAM - Université du Québec à Montréal = University of Québec in Montréal); Pierre-Charles Pradier (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Why do policyholders sometimes replace market contracting with member governance, and what does that governance change? We develop a dynamic institutional account of mutual insurance linking comparative governance, collective action, property rights, and institutional change. Relative to investor-owned entry or voice-only responses, mutual entry is most plausible when users possess group-specific coordination assets and when changing a contested insurance rule creates gains that are hard to secure through ordinary contracting. The direction of change depends on both the rule over which members acquire influence and the distribution of interests within the coalition. Success may then reshape competition and internal governance in different ways. Economic convergence depends on how readily an innovation can be transferred, whereas governance sustainability depends on the persistence of effective member control. Four historical cases show that user ownership need not create the informational or organizational resource on which a mutual relies. Its distinctive role may instead be to couple user-produced resources with control and collective benefit rights. |
| Keywords: | mutual insurance, user ownership, institutional change, cooperatives, risk governance |
| Date: | 2026–09–28 |
| URL: | https://d.repec.org/n?u=RePEc:hal:cesptp:hal-05767232 |