arXiv subjects

Wing Fung Chong

Publications and source records attributed to Wing Fung Chong.

14 recordsLinked to original sources

arXiv2026

Nash Peer-to-Peer Insurance Bargaining under Price Fairness and Coalitional Stability

We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading applied to the peer's expected loss. To justify the bargaining formulation relative to a standard fixed-weight weighted-sum optimization problem, we provide an axiomatic characterization showing that the Nash bargaining solution satisfies properties well suited to voluntary P2P insurance contracting in small pools. We establish the existence and uniqueness of the optimal contract and derive first-order characterizations for the full-, partial-, and zero-reinsurance regimes. To address subgroup formation, we develop computationally tractable sufficient conditions that rule out viable coalitional deviations, both with and without price fairness. Our numerical study investigates the impact of price fairness and pool size on the optimal contract and agents' welfare. Price fairness reduces dispersion in risk allocations and certainty-equivalent loadings among peers. Regarding pool size, welfare need not increase monotonically, highlighting that risk-pool expansion depends not only on diversification but also on the evolution of bargaining power.

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arXiv2026

Pareto Optimal Centralized Risk Sharing with Multiple Agents: Inclusivity and Fairness

This paper studies centralized risk sharing with endogenous prices. Multiple policyholders transfer risks to a central insurer through indemnity decisions, while prices are determined by pricing functionals applied to ceded risks. The resulting problem is multiobjective, with Pareto optimality as the natural efficiency criterion. We show that classical Pareto optimality may fail to reveal whether all agents are represented in a balanced decision process that scalarized objectives may assign zero weight to some agents, and group aggregates may obscure individual risk positions. Motivated by bilateral Pareto characterizations through sequential optimization, we introduce inclusive and fair Pareto optimality, a representation-based refinement requiring every agent to appear exactly once, either individually or as part of a group, in a finite ordered sequence of optimizations. Our main result proves equivalence between this concept and balanced sequential optimization, placing it between Geoffrion-proper Pareto optimality and classical Pareto optimality. An illustrative example demonstrates the framework using the Expected Shortfall.

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arXiv2026

Strategic Risk Reduction: Self-Protection and Self-Insurance

This paper studies how a risk holder should combine self-protection and self-insurance strategies when market insurance is absent. Self-protection reduces loss frequency, while self-insurance reduces loss severity. The risk holder incurs a joint risk-reduction cost that allows technological interaction between the two strategies and evaluates residual risk using either Value-at-Risk or Tail Value-at-Risk. In a Bernoulli model, we show that Value-at-Risk leads to a threshold-driven solution in which the optimal strategy is either no risk reduction, pure self-protection, or pure self-insurance, thereby exhibiting a substitution-type structure between the two risk-reduction strategies. By contrast, although Tail Value-at-Risk also admits a left-region/right-region decomposition, its left-region problem creates a direct residual frequency-severity interaction, making the local problem non-convex even in the Bernoulli setting. We solve this problem using an isoquant geometry method based on the marginal-balance curves for self-protection and self-insurance. The analysis identifies boundary, extreme constrained, touching, and crossing candidates, and shows how the confidence level and the cost technology determine whether self-protection and self-insurance behave as substitutes or complements. Illustrative examples compare the Value-at-Risk and Tail Value-at-Risk strategies, show how the confidence level changes the relevant isoquant geometry, and demonstrate that multiple crossings may generate non-unique optimal joint risk-reduction strategies.

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arXiv2026

Capital-Allocation-Induced Risk Sharing

This article proposes a new class of risk-sharing rules by exploring the relationship between capital allocation and risk sharing. While the former is concerned with ex-ante allocating capitals to different lines of business within a corporation based on the relationship among the individual risks, often also through the aggregate risk, the latter is an arrangement which collects risks from and allocates them to, also ex-ante, a group of participants. Drawing on this analogy, we introduce a novel idea of inducing risk-sharing rules by randomizing existing capital allocation principles. Such an approach derives new risk-sharing rules complementing known results in the literature, which were largely based on economic principles and Pareto optimality.

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arXiv2026

Forward Performance Processes under Multiple Default Risks

This article constructs a forward exponential utility in a market with multiple defaultable risks. Using the Jacod-Pham decomposition for random fields, we first characterize forward performance processes in a defaultable market under the default-free filtration. We then construct a forward utility via a system of recursively defined, indexed infinite-horizon backward stochastic differential equations (BSDEs) with discounting, and establish the existence, uniqueness, and boundedness of their solutions. To verify the required (super)martingale property of the performance process, we develop a rigorous characterization of this property with respect to the general filtration in terms of a set of (in)equalities relative to the default-free filtration. We further extend the analysis to a stochastic factor model with ergodic dynamics. In this setting, we derive uniform bounds for the Markovian solutions of the infinite-horizon BSDEs, overcoming technical challenges arising from the special structure of the system of BSDEs in the defaultable setting. Passing to the ergodic limit, we identify the limiting BSDE and relate its constant to the risk-sensitive long-run growth rate of the optimal wealth process.

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arXiv2025

Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach

This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {Therein, w}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {analysis} for forward investment and consumption under model uncertainty.

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arXiv2025

Cyber Risk Assessment for Capital Management

This paper introduces a two-pillar cyber risk management framework to address the pervasive challenges in managing cyber risk. The first pillar, cyber risk assessment, combines insurance frequency-severity models with cybersecurity cascade models to capture the unique nature of cyber risk. The second pillar, cyber capital management, facilitates informed allocation of capital for a balanced cyber risk management strategy, including cybersecurity investments, insurance coverage, and reserves. A case study, based on historical cyber incident data and realistic assumptions, demonstrates the necessity of comprehensive cost-benefit analysis for budget-constrained companies with competing objectives in cyber risk management. In addition, sensitivity analysis highlights the dependence of the optimal strategy on factors such as the price of cybersecurity controls and their effectiveness. The framework's implementation across a diverse range of companies yields general insights on cyber risk management.

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arXiv2024

Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents' preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal allocations of the aggregate risk in the market, and we show that the shape of the allocations depends primarily on each agent's assessment of the tail of the aggregate risk. We quantify the latter via an index of probabilistic risk aversion, and we illustrate our results using concrete examples of popular families of distortion functions. As an application of our results, we revisit the market for flood risk insurance in the United States. We present the decentralized risk sharing arrangement as an alternative to the current centralized market structure, and we characterize the optimal allocations in a numerical study with historical flood data. We conclude with an in-depth discussion of the advantages and disadvantages of a decentralized insurance scheme in this setting.

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arXiv2023

Optimal investment and consumption with forward preferences and uncertain parameters

This paper studies robust forward investment and consumption preferences within a zero-volatility context. Different from previous works, we consider an incomplete financial market model due to general investment portfolio constraints. We provide a new PDE characterization and a novel semi-explicit saddle-point construction of forward preferences and optimal strategies. We further present a more detailed construction of forward preferences and optimal strategies under constant relative risk aversion (CRRA). Key findings emphasize the necessity of a specific relationship between the initial investment preference and the forward consumption preference, indicating a long-term decreasing trend in forward consumption preference behavior.

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arXiv2023

Optimal Investment in Defined Contribution Pension Schemes with Forward Utility Preferences

Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any pre-specifications of retirement time, preferences, and market environment models do not often hold in such a prolonged horizon of the pension scheme. Pre-commitment to ensure the time-consistency of an optimal investment strategy derived from the backward model and approach leads the supposedly optimal strategy to be sub-optimal in the actual realizations. This paper revisits the optimal investment problem for the worker during the accumulation phase in the defined contribution pension scheme, via the forward preferences, in which an environment-adapting strategy is able to hold optimality and time-consistency together. Stochastic partial differential equation representation for the worker's forward preferences is illustrated. This paper constructs two of the forward utility preferences and solves the corresponding optimal investment strategies, in the cases of initial power and exponential utility functions.

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arXiv2023

Incident-Specific Cyber Insurance

In the current market practice, many cyber insurance products offer a coverage bundle for losses arising from various types of incidents, such as data breaches and ransomware attacks, and the coverage for each incident type comes with a separate limit and deductible. Although this gives prospective cyber insurance buyers more flexibility in customizing the coverage and better manages the risk exposures of sellers, it complicates the decision-making process in determining the optimal amount of risks to retain and transfer for both parties. This paper aims to build an economic foundation for these incident-specific cyber insurance products with a focus on how incident-specific indemnities should be designed for achieving Pareto optimality for both the insurance seller and buyer. Real data on cyber incidents is used to illustrate the feasibility of this approach. Several implementation improvement methods for practicality are also discussed.

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arXiv2022

Pseudo-Model-Free Hedging for Variable Annuities via Deep Reinforcement Learning

This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality actuarial market environments. In the training phase, an infant reinforcement learning agent interacts with a pre-designed training environment, collects sequential anchor-hedging reward signals, and gradually learns how to hedge the contracts. As expected, after a sufficient number of training steps, the trained reinforcement learning agent hedges, in the training environment, equally well as the correct Delta while outperforms misspecified Deltas. In the online learning phase, the trained reinforcement learning agent interacts with the market environment in real time, collects single terminal reward signals, and self-revises its hedging strategy. The hedging performance of the further trained reinforcement learning agent is demonstrated via an illustrative example on a rolling basis to reveal the self-revision capability on the hedging strategy by online learning.

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arXiv2020

Pandemic risk management: resources contingency planning and allocation

Repeated history of pandemics, such as SARS, H1N1, Ebola, Zika, and COVID-19, has shown that pandemic risk is inevitable. Extraordinary shortages of medical resources have been observed in many parts of the world. Some attributing factors include the lack of sufficient stockpiles and the lack of coordinated efforts to deploy existing resources to the location of greatest needs. The paper investigates contingency planning and resources allocation from a risk management perspective, as opposed to the prevailing supply chain perspective. The key idea is that the competition of limited critical resources is not only present in different geographical locations but also at different stages of a pandemic. This paper draws on an analogy between risk aggregation and capital allocation in finance and pandemic resources planning and allocation for healthcare systems. The main contribution is to introduce new strategies for optimal stockpiling and allocation balancing spatio-temporal competitions of medical supply and demand.

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arXiv2017

An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long maturities. We show that forward entropic risk measures converge to some constant exponentially fast. We also compare them with their classical counterparts and derive a parity result.

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