arXiv subjects

Kenneth Tsz Hin Ng

Publications and source records attributed to Kenneth Tsz Hin Ng.

7 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.

q-fin.RM↗

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.

q-fin.RM↗

arXiv2026

Pareto and Bowley Reinsurance Games in Peer-to-Peer Insurance

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses.

cs.GT↗

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.

q-fin.MF↗

arXiv2025

Mean Field Analysis of Mutual Insurance Market

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.

q-fin.RM↗

arXiv2024

Mean Field Analysis of Two-Party Governance: Competition versus Cooperation among Leaders

This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of whom interacts under a mean field game (MFG) framework. Unlike the conventional major-minor player game, the mean field term herein is endogenously affected by the two leaders simultaneously. These homogeneous followers are non-cooperative, whereas the two leaders can either compete or cooperate with each other, which are respectively formulated as a Nash and a Pareto game. The complete solutions of the leader-follower game can be expressed in terms of the solutions of some non-symmetric Riccati equations. Notably, our analysis suggests that both modes of interactions between leaders has their own merits and neither of them is always more favourable to the community of followers. In our knowledge, a comparative study of the effect of different modes of governance on the society is relatively rare in the existing literature, we here provide its first preliminary quantitative analysis; under a broad class of practically relevant models, we provide sufficient conditions to decide whether cooperation or competition between leaders is more favourable to the followers. Being in common with modern folklore, the relative merits of the two Stackelberg games depend on whether the interests between the two leaders and the followers align among themselves. Representative numerical examples are also supplemented.

math.OC↗

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.

q-fin.PM↗