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on Risk Management |
| By: | Marco Scaringi; Marco Bianchetti |
| Abstract: | Risk allocation, the decomposition of a portfolio-wide risk measure into component contributions, is a fundamental problem in financial risk management due to the non-additive nature of risk measures, the layered organizational structures of financial institutions and the range of possible allocation strategies characterized by different rationales and properties. In this work, we conduct a systematic review of the major risk allocation strategies typically used in finance, comparing their theoretical properties, practical advantages, and limitations. To this scope we set up a specific testing framework, including both simplified settings, designed to highlight basic intrinsic behaviours, and realistic financial portfolios under different risk regulations, i.e. Basel 2.5 and FRTB. Furthermore, we develop and test novel practical solutions to manage the issue of negative risk allocations and of multi-level risk allocation in the layered organizational structure of financial institutions, while preserving the additivity property. Finally, we devote particular attention to the computational aspects of risk allocation. Our results show that, in this context, the Shapley allocation strategy offers the best compromise between simplicity, mathematical properties, risk representation and computational cost. The latter is still acceptable even in the challenging case of many business units, provided that an efficient Monte Carlo simulation is employed, which offers excellent scaling and convergence properties. While our empirical applications focus on market risk, our methodological framework is fully general and applicable to other financial context such as valuation risk, liquidity risk, credit risk, and counterparty credit risk. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.12391 |
| By: | Roudari, Soheil; Ahmadian- Yazdi, Farzaneh; Namazizadeh, Ehsan; Chenarani, Hasan |
| Abstract: | This study investigates static and dynamic risk spillovers among selected assets associated with holdings affiliated with the Ministry of Cooperatives, Labor, and Social Welfare in Iran, employing the Time‑Varying Parameter Vector Autoregression (TVP‑VAR) model proposed by Antonakakis et al. (2020) during the period April 15, 2020 to April 22, 2025 . In addition, the framework of Broadstock et al. (2022) is applied to evaluate portfolio risk management efficiency, determine optimal asset weights, and compute portfolio hedge ratios based on three innovative strategies: Minimum Variance Portfolio (MVP), Minimum Correlation Portfolio (MCP), and Minimum Connectedness Portfolio (MCoP). The results reveal that Vasandogh acts as the principal transmitter and Shasta as the main receiver of volatility within the network. The analysis of cumulative portfolio returns further shows that, compared to the other two approaches, the MVP strategy delivers superior performance in optimizing cumulative returns, particularly under conditions of market instability. However, the negative dynamic cumulative returns observed in the other two strategies indicate ineffective risk management within the investment policies of the Ministry. Moreover, results related to hedge ratios demonstrate that hedging efficiency is significant only in portfolios where Shasta is included as a long‑term asset, whereas other portfolio combinations lack meaningful hedging effectiveness. Accordingly, it can be concluded that a revision of the institutional functions of the Ministry’s affiliated holdings in the financial market is essential to enhance the resilience of financial portfolios and to consider divesting loss‑making holdings as a fundamental policy priority. |
| Keywords: | Risk spillover, optimal weighting, hedging effectiveness, portfolio management, Ministry of Cooperatives, Labor, and Social Welfare |
| JEL: | G11 G14 |
| Date: | 2025–05–19 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126954 |
| By: | Roudari, Soheil |
| Abstract: | One of the primary objectives of investors is to determine the optimal asset weights and the appropriate risk‑hedging strategies considering the holding period of each asset. Accordingly, this study examines and determines the optimal investment portfolio and the dynamic risk‑hedging relationships among currency, gold coin, housing, and stock markets over the period March 2006 to February 2023, employing a Time‑Varying Parameter Vector Autoregression (TVP‑VAR) model. The results indicate that stock and currency markets act as net transmitters, while gold coin and housing markets are net receivers of volatility within the examined network. The total connectedness index reveals that during periods of sanctions and the COVID‑19 pandemic, the interdependence among these markets intensified, thereby limiting diversification opportunities within the investment portfolio. Furthermore, cumulative returns under the Minimum Variance Portfolio (MVP) approach exceed those obtained under the Minimum Connectedness Portfolio (MCOP) framework. Based on the findings, the optimal combination involves holding stocks in the short run and housing in the long run. Out of one unit of investment under normal, bearish, and bullish market conditions, 0.97, 0.96, and 0.98 units, respectively, should be allocated to this combination. The study concludes that a static view of asset behavior is not appropriate for portfolio optimization. Instead, risk‑hedging and optimal asset weighting must be considered dynamically, reflecting economic, political, and health‑related conditions. |
| Keywords: | Hedging effectiveness, time‑varying optimal weights, asset markets |
| JEL: | G11 G17 G32 |
| Date: | 2024–08–10 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126952 |
| By: | Florent Segonne |
| Abstract: | Diversification is a cornerstone of robust portfolio construction, yet its application remains fraught with challenges due to model uncertainty and estimation errors. Practitioners often rely on sophisticated, proprietary heuristics to navigate these issues. Among recent advancements, Agnostic Risk Parity introduces eigenrisk parity (ERP), an innovative approach that leverages isotropy to evenly allocate risk across eigenmodes, enhancing portfolio stability. In this paper, we review and extend the isotropy-enforced philosophy of ERP proposing a versatile framework that integrates mean-variance optimization with an isotropy constraint acting as a geometric regularizer against signal uncertainty. The resulting allocations decompose naturally into canonical portfolios, smoothly interpolating between full isotropy (closed-form isotropic-mean allocation) and pure mean-variance through a tunable isotropy penalty. Beyond methodology, we revisit fundamental concepts and clarify foundational links between isotropy, canonical portfolios, principal portfolios, primal versus dual representations, and intrinsic basis-invariant metrics for returns, risk, and isotropy. Applied to sector trend-following, the isotropy constraint systematically induces negative average-signal exposure -- a structural, parameter-robust crash hedge. This work offers both a practical, theoretically grounded tool for resilient allocation under signal uncertainty and a pedagogical synthesis of modern portfolio concepts. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.13334 |
| By: | Hyeyoon Jung; Jaehoon (Kyle) Jung |
| Abstract: | We study the economics of homeowners’ property insurance by examining how contract design balances the trade-off between incentive alignment and risk sharing. Using granular contract-level property insurance data merged with property-level disaster risk for millions of U.S. households, we develop and structurally estimate a model in which insurers optimally determine contract terms given property risk and household risk preferences. The estimates provide, to our knowledge, the first large-scale contract-level structural measures of risk aversion, risk premia, and the cost of moral hazard, allowing us to quantify how disaster risk is allocated between insurers and households. We find that the cost of moral hazard is small, yet the very mechanism used to mitigate it substantially increases households’ exposure to disaster risk: contract design leaves policyholders exposed to roughly 29 percent of total expected losses. This residual exposure is most pronounced for low-FICO households and for properties with the greatest tail risk. Counterfactuals indicate that mandating full insurance would lead to substantial market exit, increasing household vulnerability. We further show that insurers’ financial constraints are systematically correlated with the riskiness of underwritten properties and with household characteristics. |
| Keywords: | insurance; financial constraints; household finance; moral hazard; contracting |
| JEL: | C6 D8 G1 G2 G3 |
| Date: | 2025–11–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:102161 |
| By: | Osei, Prince (Center for Mathematical Economics, Bielefeld University); Riedel, Frank (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study optimal portfolio choice when the variance of asset returns is ambiguous. Building on the smooth model of ambiguity aversion by Klibanoff et al. (2005), we introduce a one-period framework in which returns follow a Variance–Gamma specification, obtained by mixing a normal distribution with a gamma prior on the variance. This structure captures empirically observed excess kurtosis and allows us to derive closed-form solutions for optimal demand. Our main results show that ambiguity about volatility leads to bounded portfolio positions, in sharp contrast to the unbounded exposures predicted by the classical CAPM when expected excess returns are large or when the mean variance tends to zero. We characterize the comparative statics of the optimal allocation with respect to risk aversion, ambiguity aversion, and the parameters of the prior distribution. For small mean excess returns, portfolio demand converges to the CAPM benchmark, indicating that ambiguity aversion affects higher-order terms only. The model provides a tractable link between robust portfolio choice and realistic, heavy-tailed return dynamics. |
| Date: | 2025–11–27 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:756 |
| By: | Paolo Varraso (DEF University of Rome "Tor Vergata") |
| Abstract: | This paper develops a quantitative heterogeneous-bank model to study how interestrate risk transmits through the financial sector. Banks optimally choose their leverage and maturity structure in the presence of limited equity issuance, default risk, and partial deposit insurance. Long-maturity assets carry a premium because they expose banks to valuation losses when interest rates rise. To preserve their franchise value, banks with low net worth relative to risky assets take on less interest-rate risk, despite the presence of risk-shifting incentives associated with deposit insurance. Applying the model to the 2022–2023 monetary tightening, I show that a rapid increase in interest rates can generate large declines in asset prices and equity values even though banks have access to shortterm assets that provide insurance against interest-rate risk. Under the lens of the model a substantial share of the losses in 2022 was predictable, whereas the losses in 2023 were largely unexpected. A shift toward long-term assets during a period of unusually low rates amplified the initial tightening, but a rebalancing toward shorter maturities dampened the transmission of later hikes. |
| Keywords: | Interest-rate risk, heterogeneous banks, aggregate uncertainty, maturity mismatch, leverage |
| JEL: | E44 G21 |
| Date: | 2025–10–11 |
| URL: | https://d.repec.org/n?u=RePEc:rtv:ceisrp:616 |
| By: | Emmanuel Lwele; Sabuni Emmanuel; Sitali Gabriel Sitali |
| Abstract: | This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms, including maximum drawdown and volatility constraints. Proximal Policy Optimization (PPO) is employed to learn adaptive asset allocation strategies over historical financial time series. Model performance is benchmarked against mean-variance and equal-weight portfolio strategies using backtesting on high-performing equities. Results indicate that the DRL agent stabilizes volatility successfully but suffers from degraded risk-adjusted returns due to over-conservative policy convergence, highlighting the challenge of balancing exploration, return maximization, and risk mitigation. The study underscores the need for improved reward shaping and hybrid risk-aware strategies to enhance the practical deployment of DRL-based portfolio allocation models. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.11481 |
| By: | Matteo Crosignani; Lina Han; Marco Macchiavelli |
| Abstract: | Firm-level geoeconomic risk can affect even broadly diversified mutual fund portfolios. We study U.S. export controls that restrict sales of cutting-edge technology to selected Chinese firms for national security reasons. The stock prices of affected domestic suppliers drop immediately after the policy introduction. Mutual funds holding these stocks experience increased volatility and lower returns. Fund managers respond by selling stocks of exporters to China, buying lottery-like stocks, and increasing portfolio concentration. While stock-picking and market-timing skills do not help, specialist and high-fee funds are better at navigating geoeconomic risk. |
| Keywords: | mutual funds; Asset allocation; geoeconomic risk; Export controls |
| JEL: | G12 F51 F38 |
| Date: | 2025–11–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:102163 |
| By: | Xuzhu ZHENG (Graduate School of Economics, The University of Osaka); Masato UBUKATA (The Faculty of Economics, Meiji Gakuin University); Kosuke OYA (Graduate School of Economics, The University of Osaka, Center for Mathematical Modeling and Data Science, The University of Osaka) |
| Abstract: | This study examines the existence of rough volatility, which has recently attracted considerable attention and is characterized by volatility dynamics that cannot be fully captured by conventional volatility models. Specifically, we investigate whether the observed roughness in volatility is merely an artifact induced by microstructure noise inherent in high-frequency price data, or whether such rough behavior persists even after accounting for the effects of noise. The empirical analysis utilizes high-frequency data from the Nikkei 225 index as well as two representatives, actively traded individual stocks. Applying several representative volatility estimation methods, we first construct volatility series and then estimate their Hurst exponents using a nonparametric estimation procedure proposed in the literature. Our results show that, regardless of the presence of microstructure noise, the estimated Hurst exponents consistently take low values, suggesting that the volatility processes under study exhibit rough behavior. These findings provide supporting evidence for the necessity of incorporating roughness into volatility modeling to achieve a more refined understanding of volatility dynamics in financial markets. |
| Keywords: | High-frequency data, Volatility, Roughness |
| JEL: | C14 C55 C58 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:osk:wpaper:2517 |
| By: | Tim J. Boonen; Engel John C. Dela Vega |
| Abstract: | This paper considers an insurer with two collaborating business lines that must make three critical decisions: (1) dividend payout, (2) a combination of proportional and excess-of-loss reinsurance coverage, and (3) capital injection between the lines. The reserve level of each line is modeled using a diffusion approximation, with the insurer's objective being to maximize the weighted total discounted dividends paid until the first ruin time. We obtain the value function and the optimal strategies in closed form. We then prove that the optimal dividend payout strategy for bounded dividend rates is of threshold type, while for unbounded dividend rates it is of barrier type. The optimal combination of proportional and excess-of-loss reinsurance is shown to be pure excess-of-loss reinsurance. We also show that the optimal level of risk ceded to the reinsurer decreases as the aggregate reserve level increases. The optimal capital injection strategy involves transferring reserves to prevent the ruin of one line. Finally, numerical examples are presented to illustrate these optimal strategies. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.11383 |
| By: | Sven Damen; Matthijs Korevaar; Stijn Van Nieuwerburgh |
| Abstract: | Residential properties with the lowest rent levels provide the highest investment returns to their owners. Using detailed rent, cost, and price data from the United States, Belgium, and The Netherlands, we show that this phenomenon holds across housing markets and time. If anything, low-rent units hedge business cycle risk. We also find no evidence for differential regulatory risk exposure. We document segmentation of investors, with large corporate landlords shying away from the low-tier segment possibly for reputational reasons. Financial constraints prevent renters from purchasing their property and medium-sized landlords from scaling up, sustaining excess risk-adjusted returns. Low-income tenants ultimately pay the price for this segmentation in the form of a high rent burden. |
| Keywords: | Affordable Housing; Market Segmentation; Rental market; risk and return in housing |
| JEL: | R3 |
| Date: | 2025–01–01 |
| URL: | https://d.repec.org/n?u=RePEc:arz:wpaper:eres2025_201 |
| By: | Ferreira Batista Martins, Igor (Örebro University School of Business); Virbickaitè, Audronè (CUNEF University, Madrid, Spain); Nguyen, Hoang (Linköping University); Freitas Lopes, Hedibert (nsper Institute of Education and Research, Sao Paulo, Brazil) |
| Abstract: | We propose a high-frequency stochastic volatility model that integrates persistent component, intraday periodicity, and volume-driven time-of-day effects. By allowing intraday volatility patterns to respond to lagged trading activity, the model captures economically and statistically relevant departures from traditional intraday seasonality effects. We find that the volumedriven component accounts for a substantial share of intraday volatility for futures data across equity indexes, currencies, and commodities. Out-of-sample, our forecasts achieve near-zero intercepts, unit slopes, and the highest R2 values in Mincer-Zarnowitz regressions, while horserace regressions indicate that competing forecasts add little information once our predictions are included. These statistical improvements translate into economically meaningful gains, as volatility-managed portfolio strategies based on our model consistently improve Sharpe ratios. Our results highlight the value of incorporating lagged trading activity into high-frequency volatility models. |
| Keywords: | Intraday volatility; high-frequency; volume; periodicity. |
| JEL: | C11 C22 C53 C58 |
| Date: | 2025–11–21 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:oruesi:2025_014 |
| By: | Mainak Singha |
| Abstract: | We document a high-performing cross-sectional equity factor that achieves out-of-sample Sharpe ratios above 13 through regime-conditional signal activation. The strategy combines value and short-term reversal signals only during stock-specific drift regimes, defined as periods when individual stocks show more than 60 percent positive days in trailing 63-day windows. Under these conditions, the factor delivers annualized returns of 158.6 percent with 12.0 percent volatility and a maximum drawdown of minus 11.9 percent. Using rigorous walk-forward validation across 20 years of S&P 500 data (2004 to 2024), we show performance roughly 13 times stronger than market benchmarks on a risk-adjusted basis, produced entirely out-of-sample with frozen parameters. The factor passes extensive robustness tests, including 1, 000 randomization trials with p-values below 0.001, and maintains Sharpe ratios above 7 even under 30 percent parameter perturbations. Exposure to standard risk factors is negligible, with total R-squared values below 3 percent. We provide mechanistic evidence that drift regimes reshape market microstructure by amplifying behavioral biases, altering liquidity patterns, and creating conditions where cross-sectional price discovery becomes systematically exploitable. Conservative capacity estimates indicate deployable capital of 100 to 500 million dollars before noticeable performance degradation. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.12490 |
| By: | Jian'an Zhang |
| Abstract: | We study reinforcement learning (RL) on volatility surfaces through the lens of Scientific AI. We ask whether axiomatic no-arbitrage laws, imposed as soft penalties on a learned world model, can reliably align high-capacity RL agents, or mainly create Goodhart-style incentives to exploit model errors. From classical static no-arbitrage conditions we build a finite-dimensional convex volatility law manifold of admissible total-variance surfaces, together with a metric law-penalty functional and a Graceful Failure Index (GFI) that normalizes law degradation under shocks. A synthetic generator produces law-consistent trajectories, while a recurrent neural world model trained without law regularization exhibits structured off-manifold errors. On this testbed we define a Goodhart decomposition \(r = r^{\mathcal{M}} + r^\perp\), where \(r^\perp\) is ghost arbitrage from off-manifold prediction error. We prove a ghost-arbitrage incentive theorem for PPO-type agents, a law-strength trade-off theorem showing that stronger penalties eventually worsen P\&L, and a no-free-lunch theorem: under a law-consistent world model and law-aligned strategy class, unconstrained law-seeking RL cannot Pareto-dominate structural baselines on P\&L, penalties, and GFI. In experiments on an SPX/VIX-like world model, simple structural strategies form the empirical law-strength frontier, while all law-seeking RL variants underperform and move into high-penalty, high-GFI regions. Volatility thus provides a concrete case where reward shaping with verifiable penalties is insufficient for robust law alignment. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.17304 |
| By: | Luis Herrera (BANCO DE ESPAÑA); Mara Pirovano (EUROPEAN CENTRAL BANK); Valerio Scalone (EUROPEAN CENTRAL BANK) |
| Abstract: | This paper introduces the Risk-to-Buffer approach for calibrating the countercyclical capital buffer (CCyB), with a particular emphasis on the positive neutral (PN) CCyB rate, tailored to the euro area. The proposed methodology is applied in both a dynamic stochastic general equilibrium (DSGE) framework and a macroeconomic time series setting. It estimates the amplification of adverse shocks under varying levels of cyclical systemic risk and calibrates the CCyB to counteract these amplification effects. Using data from 2009 to 2023, the analysis suggests a positive neutral CCyB rate for the euro area ranging between 1% and 1.5%. The findings indicate that output and inflation shocks, which are not directly linked to the materialization of domestic systemic risk, and high degrees of trade openness, warrant a more prominent role of the PN CCyB in the overall CCyB calibration. The exercise to illustrate the methodology is carried out for the euro area. While national calibrations require additional exercises, this approach offers a flexible and complementary framework that can support and enhance national-level analyses. |
| Keywords: | financial stability, macroprudential policy, capital requirements, countercyclical capital buffer |
| JEL: | C32 E51 E58 G01 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:bde:wpaper:2544 |
| By: | Jiacheng Wu |
| Abstract: | A theoretical model of systemic-risk propagation of financial market is analyzed for stability. The state equation is an unsteady diffusion equation with a nonlinear logistic growth term, where the diffusion process captures the spread of default stress between interconnected financial entities and the reaction term captures the local procyclicality of financial stress. The stabilizing controller synthesis includes three steps: First, the algebraic Riccati equation is derived for the linearized system equation, the solution of which provides an exponentially stabilizing controller. Second, the nonlinear system is treated as a linear system with the nonlinear term as its forcing term. Based on estimation of the solutions for linearized equations and the contraction mapping theorem, unique existence of the solution for the nonlinear system equation is proved. Third, local asymptotic stability of the nonlinear system is obtained by considering the corresponding Hamilton-Jacobi equation. In both the linearized and nonlinear systems, the resulting controllers ensure that the $H^{\infty}$ norms of the mappings from disturbance to the output are less than a predefined constant. Stabilizing conditions provide a new framework of achieving system-level financial risk managing goals via the synergy of decentralized components, which offers policy-relevant insights for governments, regulators and central banks to mitigate financial crises. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.11909 |
| By: | Xianglin Sun; Sven Damen |
| Abstract: | Flooding represents a major natural hazard with significant economic consequences. We study the causal effect of the introduction of a mandatory flood risk disclosure policy in Flanders in 2013, which introduced explicit flood risk labels in property listings. Leveraging extensive transaction data and employing Difference-in-Differences (DiD) and Difference-in-Discontinuity (Diff-in-Disc) methods, we assess the policy's influence on housing prices. Our results reveal that properties located in potential flood risk zones experienced price declines of up to 4.71%, suggesting heightened market sensitivity to disclosed flood risks. However, for properties in effective flood risk zones, we find no consistent impact, likely reflecting existing awareness of flood exposure. These findings highlight the effectiveness of mandatory disclosure in mitigating information asymmetries and contribute to the broader discourse on environmental risk communication and housing market behavior. |
| Keywords: | flood risk; housing market; Mandatory Disclosure Policy |
| JEL: | R3 |
| Date: | 2025–01–01 |
| URL: | https://d.repec.org/n?u=RePEc:arz:wpaper:eres2025_222 |
| By: | Anahit Poghosyan (Central Bank of Armenia); Gevorg Minasyan (Central Bank of Armenia) |
| Abstract: | This paper examines whether financial behaviour, defined through credit history and current debt burden, can improve the modelling of automobile accident risk. Drawing on rich administrative data from Armenia's compulsory motor third party liability insurance system (CMTPL) combined with credit registry records, the study finds that weaker repayment histories are strongly associated with higher accident probabilities and larger claim amounts, potentially reflecting core behavioural traits that carry over into driving behaviour. Indicators of short-run financial strain add further explanatory power by capturing situational pressures not reflected in long-run patterns, with accident risk peaking when adverse credit histories coincide with elevated financial burden. These relationships hold across a range of empirical approaches - including negative binomial models and a monthly driver-level panel that accounts for congestion, weather, and other time-specific conditions - and they remain robust once driver income is included. In the panel estimates, both between-driver and within-driver components remain significant, indicating that even for the same individual, a deterioration in credit history or an increase in financial burden corresponds to a material rise in accident risk. In terms of distributional effects, Tweedie-based simulations show that gains in pricing accuracy come with disproportionate premium increases for financially vulnerable households, highlighting a central efficiency-equity trade-dilemma for regulators. |
| Keywords: | Credit History, Financial Distress, Driving Risk, Claim Severity, Credit-Based Underwriting |
| JEL: | G22 D14 D12 C23 C25 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:ara:wpaper:wp-2025-03 |
| By: | Bohan Li; Wenyuan Li; Kenneth Tsz Hin Ng; Sheung Chi Phillip Yam |
| Abstract: | A mutual insurance company (MIC) is a type of consumer cooperative owned by its policyholders. By purchasing insurance from an MIC, policyholders effectively become member-owners of the company and are entitled to a share of the surplus, which is determined by their own collective claims and premium contributions. This sharing mechanism creates an interactive environment in which individual insurance strategies are influenced by the actions of others. Given that mutual insurers account for nearly one-third of the global insurance market, the analysis of members' behavior under such a sharing mechanism is of both practical and theoretical importance. This article presents a first dynamic study of members' behavior in the prevalent mutual insurance market under the large-population limit. With members' wealth processes depending on the law of the insurance strategies, we model the surplus-sharing mechanism using an extended mean field game (MFG) framework and address the fundamental question of how strategic interactions in this setting influence individual decisions. Mathematically, we establish the global-in-time existence and uniqueness of the mean field forward-backward stochastic differential equation (MF-FBSDE) characterizing the Nash equilibrium strategy, employing techniques to accommodate realistic insurance constraints. Computationally, we develop a modified deep BSDE algorithm capable of solving the extended MFG problem with an additional fixed-point structure on the control. Utilizing this scheme, we examine how structural features of the MIC's design, such as the composition of risk classes and surplus-sharing proportions, reshape members' decisions and wealth through collective interactions, underscoring the central role of these mechanisms in MICs. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.12292 |
| By: | Mikhail Pomazanov |
| Abstract: | The proposed work shows how to determine the Loss Given Default (LGD) after default without preparing a separate model. This requires the following: LGD model before default, the calculation of the average repayment time after default, the values of the volumes and moments of repayments after default, along with the lending rate for each loan, and the recovery rate recorded in the default volume. The LGD(t) variant is proposed, which predicts recovery based on the estimation of the average posterior distribution. An analysis is conducted on recovery portfolios, demonstrating the approximate statistics of the desired quantity. The solution allows you to build an LGD model after default for any default loans, provided that you know the volumes, repayment dates, and interest rates. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.11364 |