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on Risk Management |
| By: | Yichi Zhang; Ke Zhu; Zhoufan Zhu |
| Abstract: | Learning Value-at-Risk (VaR) and Expected Shortfall (ES) is important for managing financial risks effectively. Existing approaches with limited parameters are vulnerable to model misspecification in the era of big data. To address this limitation, we propose a large tail risk model, the retrieval-enhanced self-grouping autoencoder (ReSGA), which is designed with millions of parameters to exploit the rich cross-sectional dependence and long-term temporal dynamics of assets using their characteristics. Applied to monthly US equity returns from 1926 to 2023 with 153 firm characteristics, ReSGA outperforms twelve econometric and machine learning competitors in terms of out-of-sample loss and statistical backtesting. In addition, its forecast advantages can translate into significant economic gains from long-short decile portfolios that are constructed by a new size-enhanced left-side momentum strategy. To clarify the role of complexity, we further conduct a systematic scaling analysis and demonstrate that improvements in joint VaR-ES forecasting are primarily driven by data complexity rather than model complexity. Finally, our analyses of group-importance and transfer-learning exhibit the interpretability and cross-market generalizability of ReSGA. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.04576 |
| By: | Suresh, Karthik Ramakrishna |
| Abstract: | This paper introduces the G-spread, a measure of permanent capital loss risk offered as an alternative to the price-based metrics that dominate contemporary finance: the Capital Asset Pricing Model, Value-at-Risk, beta, standard deviation, and the Fama-French multi-factor model. The G-spread quantifies the return a business earns above its weighted average cost of capital after accounting for reinvestment requirements, incorporating a terminal-growth adjustment calibrated to an AI-era operating environment. The central argument is epistemological: price-based models measure volatility, whereas the risk that matters to long-horizon equity investors is the permanent loss of capital. Because the two are weakly correlated, volatility-based models can misclassify structurally sound businesses as risky and structurally fragile ones as safe. Using eleven worked examples from Indian equity markets and a 227-company retrospective study spanning India, the United States, China, and Japan, the paper tests whether the G-spread identifies the direction of long-run value creation and destruction more reliably than the price-based benchmarks. Across the four markets, holdings flagged EXCLUDED by the financial-health gates returned an average of −12.9% per year, beating the benchmark in only 2% of cases, while holdings classified LOW RISK delivered average excess returns of 10.8 percentage points above the benchmark, beating it 93% of the time. The findings suggest that grounding risk measurement in business economics rather than price behaviour better captures the loss exposure long-term investors actually bear. |
| Keywords: | permanent capital loss, risk measurement, weighted average cost of capital, reinvestment, terminal growth, CAPM, value-at-risk, Fama-French, value investing, Indian equities, cross-market study |
| JEL: | G11 G12 G15 G17 G32 |
| Date: | 2026–06–02 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129370 |
| By: | Christopher Blier-Wong; Jean-Gabriel Lauzier |
| Abstract: | While risk pooling lowers the total cost of risk, efficiency alone does not make a pool viable. Participants need terms that ensure their participation, that are immune to subgroups breaking away, and that allow new members to join. Under cash-additive risk measures, the minimum cost of a coalition's risk determines the value created by that coalition, and deterministic side payments redistribute that value among participants. Institutional risk sharing is thus a transferable-utility cooperative game. We prove that the game is totally balanced whenever the risk measures are convex (agents are risk averse), so every coalition has a nonempty core and stable allocations always exist. We then analyze entry monotonicity through Population-Monotonic Allocation Schemes (Sprumont, 1990), a strong requirement that is notoriously difficult to construct and has received limited attention in risk sharing. We find several structural conditions that ensure that either the Arrow--Debreu pricing surplus allocation rule or the proportional-cost surplus allocation rule satisfies this entry-monotonicity property, the latter being a novel cooperative notion we propose. These verifiable structural conditions naturally arise in pooled (re)insurance and credit portfolios, providing pool designers with a practical toolkit for building risk pools that remain stable and attractive as they expand. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.00972 |
| By: | Costa-Font, Joan; Courbage, Christophe; Raut, Nilesh |
| JEL: | J1 |
| Date: | 2026–05–28 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:138650 |
| By: | Mustafin, Damir |
| Abstract: | As the foundation of the economic system, the real sector is particularly susceptible to risks associated with shifting market conditions, technological failures, fluctuations in resource prices, and regulatory and geopolitical factors. In the current environment, effective risk management has assumed critical importance and necessitates the utilization of advanced digital technologies. This article explores the potential for applying digital solutions to risk management within the real sector. It outlines general approaches to risk management in the real sector and describes the digital transformation tools applicable to this field. The methodological potential for risk forecasting, analysis, and control—facilitated by digital technologies—is characterized. Furthermore, key directions for the digitalization of risk management are identified. The findings of this study can be utilized in formulating programs aimed at enhancing the resilience of real-sector enterprises and minimizing the adverse consequences of economic uncertainty. Keywords: economic development, risk management, real sector, digital solutions, forecasting, analytics, control. |
| Date: | 2025–03–11 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:uy38v_v1 |
| By: | Mario V. W\"uthrich |
| Abstract: | The balance property is an important property of fitted statistical models deployed for insurance pricing. It guarantees that the total actuarial price in the fitted model is equal to the totally observed loss used to fit the model. This can be seen as an in-sample global unbiasedness property. Maximum likelihood fitted generalized linear models (GLMs) with canonical links automatically fulfill the balance property. Lindholm-W\"uthrich (Scandinavian Actuarial Journal, 2026) discussed two popular balance correction methods in case the balance property fails to hold. This note extends this discussion with a third method, constrained GLM fitting, that turns out to be superior over the two previously discussed ones. Moreover, we highlight the connection between the balance property and ex-post risk sharing rules. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.07276 |
| By: | Paul H.S. Kim; Anran Li |
| Abstract: | We study the role of public risk-sharing in markets where firms face substantial cost uncertainty, focusing on public reinsurance in health insurance. We develop a model where insurers internalize cost uncertainty through risk charges that raise effective marginal costs, and create a role for reinsurance. Public reinsurance lowers both expected costs and cost volatility, particularly for smaller insurers, reducing prices and enhancing competition. Using an event study of staggered state-level reinsurance programs, we show that public reinsurance leads insurers to lower prices and private reinsurance purchases, benefiting financially constrained insurers the most. Structural estimates indicate that risk charges account for a substantial share of the premium-cost wedge, and highlight public reinsurance's comparative advantage over premium subsidies by providing risk protection and enhancing competition. Our results underscore the importance of accounting for firms' risk exposure in policy design and provide a general framework for understanding public risk-sharing policies. |
| JEL: | I0 L0 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35282 |
| By: | Daniil Peysakhovich; Rafa{\l} Sieradzki |
| Abstract: | Errors in risk valuation outputs arising from data-feed failures, model misconfiguration, or system malfunctions can propagate undetected through an investment bank's risk infrastructure and generate material operational losses. Using proprietary daily credit-derivatives data from a major global investment bank covering 183 trades across 129 trading days, we design, implement, and empirically evaluate the Ensemble Quality Assessment Framework (EQAF), a layered unsupervised architecture that combines complementary outlier-detection methods to monitor risk calculation integrity in real time. Using a controlled anomaly-injection protocol with eight operationally realistic scenarios, we show that the calibrated ensemble achieves F1 scores of 61-79%, substantially outperforming the best individual method (6-66%) across four distinct risk-measure datasets. Improvements of 4-6 percentage points in AUC-ROC confirm that this advantage is robust to threshold selection. We further demonstrate that purely statistical detection methods systematically fail to identify stale-value anomalies, a class of frozen-feed errors in which valuation outputs are identical to prior observations and therefore indistinguishable from normal data, and that domain-specific deterministic rules are architecturally indispensable. These findings have direct implications for model risk management under Basel III and the Fundamental Review of the Trading Book (FRTB), where automated and auditable quality controls for internal risk models are increasingly required. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.20079 |
| By: | Xinyue Fang; Robert \'Slepaczuk |
| Abstract: | This study investigates whether regime-dependent volatility forecasting and machine-learning-based return prediction can be jointly integrated to improve both statistical forecasting performance and economic strategy outcomes in equity markets. Using high-frequency CSI 300 Index data from 2005 to 2023, a sequential twostage framework is developed. In the first stage, realized volatility is modeled using regime-augmented HARQ specifications combined with Markov-switching GJR-GARCH filtering to capture long-memory dynamics, asymmetry, and structural market regimes. In the second stage, volatility forecasts, regime indicators, and return-related predictors are incorporated into an XGBoost return-prediction model estimated through a strictly walk-forward out-of-sample procedure. The empirical results demonstrate that regime-aware volatility forecasting consistently outperforms baseline HARQ models across forecast evaluation metrics and is generally supported by formal forecast comparison tests. In contrast, return predictability remains weak, state-dependent, and concentrated primarily in low-volatility regimes. Although naive predictive trading strategies generally fail after accounting for realistic transaction costs, carefully designed implementations incorporating volatility scaling, low-volatility gating, threshold calibration, and turnover controls can improve defensive economic performance. The findings suggest that the practical value of predictive systems in financial markets may depend less on generating strong unconditional return forecasts and more on transforming weak state-dependent signals into economically robust portfolio allocation rules. Overall, the study contributes by integrating econometric volatility modeling, regime classification, machine-learning return prediction, and implementation realism within a unified framework. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.09478 |
| By: | Appelbaum, Elie |
| Abstract: | This paper develops a theoretical model of decision-making under risk in which the agent is a union of individuals with heterogeneous attitudes toward risk. The risk attitude governing the joint decision is endogenously determined as a compromise between individuals' innate preferences, with deviations generating costs. The chosen risk attitude affects the optimal portfolio and, therefore, the risk premium associated with exposure to uncertainty. The analysis shows that the optimal compromise equates the marginal increase in the risk premium with the marginal reduction in deviation costs. Because risk attitudes and portfolio choices are jointly determined, parameter changes affect both sides of this condition, generating feedback effects that may lead to ambiguous or non-monotone comparative statics. The framework provides a tractable approach to modelling endogenous risk attitudes in collective decision-making under uncertainty. |
| Keywords: | household portfolio choice; heterogeneous risk preferences; Endogenous risk attitudes; collective decision making; preference aggregation. |
| JEL: | C18 C44 D80 D81 I10 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129118 |
| By: | Mintod\^e Nicod\`eme Atchad\'e; Marcus C. Christiansen; Friedrich Hubalek; Gero Junike |
| Abstract: | The surplus of a life insurance policy depends on both systematic changes in mortality risk and financial changes. We propose to decompose the surplus by the axiomatically justified IASU decomposition, which is a continuous time version of the Shapley value. However, life tables are not updated continuously, but rather, only once per year. In this yearly update cycle of the life tables, we apply different interpolation methods to perform the IASU decomposition and analyze the effects of these methods on the surplus decomposition. Our results show that Lee-Carter and linear interpolation yield almost identical decompositions, whereas constant approximations results in substantially different decompositions. As a consequence, reporting standards and regulators should clarify how to interpolate mortality risks. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.04715 |
| By: | Symeon Vaidanis; Marios Kountouris |
| Abstract: | This paper develops a binary-gamble framework for characterizing risk sensitivity and loss aversion in Cumulative Prospect Theory (CPT). The proposed probabilistic risk-sensitivity metric is defined as a probability-threshold ratio that determines acceptance and preference thresholds in choice problems involving either a certain outcome and a binary gamble or two binary gambles. We show how standard notions of symmetric and non-symmetric bet aversion can be recovered within this framework, and we compare the resulting threshold-based conditions with utility premia, probability premia, and Arrow--Pratt curvature measures. The analysis clarifies when these criteria coincide and when they diverge, particularly for increasing aversion conditions, binary gambles with unequal probability distributions, and settings involving probability weighting functions. We also identify technical restrictions that arise when CPT-utility functions are used to represent loss aversion at the reference point. The resulting framework provides a decision-theoretic interpretation of risk sensitivity that is directly tied to probability thresholds and complements existing premium-based approaches. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.06652 |
| By: | Wagner, Leandro |
| Abstract: | Liquidity is central to modern fixed-income markets, yet it is often treated too simply. Bonds are commonly described as liquid or illiquid, as though liquidity were a fixed quality built into the security itself. This book challenges that view. It argues that liquidity is not a permanent feature of a bond, but a fragile condition created by market structure, financing arrangements, collateral rules, dealer capacity, valuation practices, regulation, and investor behaviour. The Endogeneity of Liquidity Risk in Leveraged Fixed-Income Systems develops a clear theory of how liquidity is created inside the financial system and how it can disappear under stress. A bond may appear easy to sell in calm markets, financeable through repo, acceptable as collateral, and stable in daily valuation. Yet those qualities may depend on conditions that change quickly when volatility rises, funding tightens, or many investors try to exit at the same time. |
| Keywords: | Liquidity Risk Endogeneity Leveraged Finance Fixed-Income Markets Systemic Risk Market Liquidity Funding Liquidity Financial Stability Bond Markets Leverage Cycles Liquidity Spirals Asset Fire Sales Margin Constraints Financial Contagion Macroprudential Regulation Market Microstructure Credit Markets Repo Markets Risk Transmission Stress Dynamics Fragility Procyclicality Capital Markets Dealer Intermediation Liquidity Shocks |
| JEL: | D0 H3 O1 |
| Date: | 2026–03–03 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129114 |
| By: | Nicholas-James Clavet; Pierre-Carl Michaud; Julien Navaux |
| Abstract: | We develop a model of optimal long-term care provision and insurance with heterogeneous risk and preferences. Using a novel survey experiment, we estimate preferences (demand) for care settings and service bundles. We then calibrate health transitions and the supply of services using Canadian administrative data for the province of Quebec. The optimal insurance scheme has lower co-insurance in nursing homes and higher co-insurance in home care while leading to a constrained expansion of home care services. Relative to the prevailing system in Quebec, optimal provision increases home care utilization, raises public expenditure threefold, and delivers a large increase in consumer surplus. |
| Keywords: | long-term care, insurance, preferences, risk, supply constraints. |
| JEL: | H51 I18 J14 J26 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:rsi:cjpcha:07 |
| By: | Palligkinis, Spyros; Jo, Jae Hyun; Demartis, Stefano |
| Abstract: | We assess the effectiveness of supervisory activities in mitigating credit risk stemming from banks’ commercial real estate portfolios. We analyse two activity types deployed by European banking supervisors: (a) on-site inspections, which assess in depth banks’ risk-taking and internal controls, but can only be selectively applied, and (b) off-site targeted reviews, which survey risk management practices across institutions, are less intrusive but are applied more widely. Using quarterly confidential supervisory data for large euro area banks between 2020 and 2024, we employ a Difference-in-Differences framework with an event-study design to capture the effects of these activities on the coverage ratio of banks’ commercial real estate portfolios. We find that on-site inspections are followed by persistent increases in coverage ratios, while targeted reviews are associated with immediate improvements which are significant but short-lived. The results highlight the complementary nature of the two activity types, which have different outreach possibilities and effects. JEL Classification: G21, G28, R30, C23 |
| Keywords: | bank provisioning, commercial real estate, supervisory activities, supervisory effectiveness |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263247 |
| By: | Andrea Molent |
| Abstract: | This paper develops a valuation framework for guaranteed lifetime withdrawal benefit (GLWB) contracts with long-term care (LTC) features when the reference fund follows exponential Levy dynamics and the short rate follows the Hull-White model. The contract combines financial guarantees, longevity protection, health-contingent LTC payments, and surrender optionality, requiring the joint treatment of jump risk, stochastic discounting, and disability risk. The numerical method couples a recombining Hull-White trinomial tree with an implicit-explicit (IMEX) finite difference scheme. The framework incorporates a seven-state health model, annual fees, LTC payments, guaranteed withdrawals, and bang-bang policyholder actions, and is benchmarked against Monte Carlo simulation. Numerical results show that the hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks. They also show that Levy equity dynamics and stochastic interest rates have a material impact on fair fees and surrender incentives, and affect the decomposition of contract value. The findings highlight the importance of modelling financial tail risk and interest-rate risk jointly when pricing long-term insurance guarantees with LTC-contingent benefits. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.30567 |
| By: | Yifan Hong; Hongmiao Fan; Chen Wang |
| Abstract: | Decision-making under risk is typically studied through single-shot lottery choices. Yet many real decisions involve combinatorial risk, where risk arises from multiple risky components, so the lottery over outcomes is induced rather than given outright and can be costly to evaluate exactly. We introduce an investment-allocation task to study decision under combinatorial risk, where investing in a component raises its success probability and thereby reshapes the outcome distribution. Participants favor the option with the larger probability increment, and, when increments are equal, the option with the higher initial success probability. Revealing the induced probability mass function (PMF) substantially changes behavior, making participants less responsive to combinatorial-risk features and reducing choice variance. To explain these patterns, we move beyond standard benchmarks and hand-crafted hypotheses with symbolic regression to discover compact descriptive models. The discovered models rely mainly on combinatorial-risk features, such as the after-investment success probability, rather than exact evaluation of the full induced distribution. Behavior under the displayed PMF is then well explained by augmenting this model with a prospect-theoretic residual model. The results show that people navigate combinatorial risk primarily through its core features, shifting toward lottery valuation only when the induced PMF is displayed. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.10092 |
| By: | Akash Deep; Nicholas Appiah; Svetlozar T. Rachev |
| Abstract: | This paper studies the joint role of long-memory dynamics, rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions to examine whether persistence measures contain economically meaningful forecasting information beyond conventional volatility predictors. Using a panel of 115 S&P500 constituents from November 2001 through April 2026, we document that volatility proxies exhibit substantial long-memory behavior and locally rough dynamics. The cross-sectional mean Geweke-Porter-Hudak estimate of the memory parameter is $\hat{d} = 0.226$, while the corresponding local-Whittle estimate is $\hat{d} = 0.440$, with statistical significance observed across nearly the entire panel. Rolling estimates of persistence rise substantially during the global financial crisis and the COVID period and display a positive contemporaneous association with the VIX. We then examine whether persistence-related features improve out-of-sample volatility forecasts beyond standard HAR and HAR-X benchmarks. Incorporating cross-sectional persistence aggregates, sectoral persistence measures, and persistence-by-stress interaction terms produces moderate but statistically significant forecasting improvements, particularly at longer horizons and during stress regimes. Forecast gains are strongest during periods of elevated market volatility and in volatility-managed portfolio applications. The results suggest that persistence measures may serve as useful reduced-form indicators of the duration and propagation of uncertainty in financial markets, although the paper does not claim structural identification of the economic mechanisms generating persistence. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.24285 |
| By: | Ryan McCrickerd |
| Abstract: | This article introduces an unconventional model for price processes in finance that emerges from the classical Heston model under Mechkov's fast-reversion limit. This new fast-excursion Heston model exhibits instantaneous (i.e. fast) excursions through an interval of prices at each time, which are invisible to vanilla options but critical for hitting probabilities and continuously monitored exotics. Theoretically, the model provides a rare example of a non-degenerate limit of stochastic volatility models that escapes the Skorokhod topologies. This leads us to a class of interval-valued processes which exist as lifts of subordinated Levy processes, through the concept of selections in the theory of random closed sets. On the practical side, we show how the model can be simulated using price-time parametric representations, and utilise a purpose-built classical Heston simulation scheme in order to visualise convergence. Finally we demonstrate how this model raises hitting probabilities for barrier options considerably (of order 10% for one-month EURUSD options), due to taking excursion risk into account. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.06737 |