Abstract This paper proposes a game-theoretic model that captures the interaction between price competition and risk heterogeneity in the insurance market. In this competitive game, each insurer sets a best-response premium to maximize the expected utility of its terminal wealth. We model heterogeneity between two distinct types of potential policyholders within a collective risk framework. We develop a Markovian structural demand model to capture how the expected number of policies is influenced by insurers’ premiums in a heterogeneous market. Within the non-cooperative game setting, we provide a sufficient condition to guarantee the existence of a pure-strategy Nash equilibrium. Several numerical examples, including a sensitivity analysis and repeated one-period myopic game extension, are provided to illustrate the implications of risk heterogeneity under competitive insurance pricing.
Abstract In this paper, we develop an innovative framework for reinsurance contracting problem under model ambiguity. The insurer and the reinsurer take the roles of demander and supplier in reinsurance market, respectively. Both parties aim to maximize their respective alpha α $\alpha$ -maxmin mean-variance performance functional. They choose optimal reinsurance policies, and the equilibrium reinsurance price is determined by clearing the market for demand and supply. The reinsurance premium is calculated according to the variance premium principle. For tractability, we apply the second-order approximation to the entropic penalty for ambiguity. By solving the extended Hamilton–Jacobi–Bellman equation system within the game-theoretic framework, the semi-explicit expressions for the equilibrium reinsurance demand-supply strategy and the reinsurance price have been derived. A key finding is that when both players are ambiguity-averse, a unique equilibrium reinsurance price always exists; by contrast, with ambiguity-seeking/neutral preferences, a market equilibrium reinsurance price may fail to exist.
Abstract Nonlife insurance lines often exhibit strong interdependencies due to systemic risks, affecting pricing, reserving, and capital allocation. This paper examines optimal premium setting for a multiline insurer under demand-based pricing, incorporating dependence structures by integrating Lévy copulas into a stochastic optimization framework in which a risk-averse insurer maximizes the expected discounted lifetime utility of consumption. The insurer is a monopolistic price setter that influences demand and claim arrival rates through premium adjustments. The optimization problem resembles a multiproduct monopolist with a nonseparable cost function driven by claim dependence. For the case of two-line insurers, we establish conditions under which higher dependence increases risk exposure and reduces profitability, using supermodular ordering techniques. Numerical results using a Clayton–Lévy copula demonstrate how dependence intensity and risk aversion impact optimal pricing strategies.
Abstract Accurate modeling of the loss distributions is crucial for solvency capital assessment and reinsurance pricing. Conventional single-component models fail to capture the dual nature of insurance data, which consists of a high-frequency body and a heavy tails of extreme losses. This paper introduces a novel composite Weibull–Pareto model with a smooth logistic transition in the hazard rates by avoiding discontinuities. We compare frequentist (maximum likelihood) and the Bayesian estimation using weakly informative and empirical priors to assess parameter uncertainty and tail risk. Using the canonical Danish Fire Insurance dataset, the results indicate that Bayesian inference delivers superior predictive performance and conservative estimates of the extreme tail-risk measures such as Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR). Maximum likelihood estimates appear overly optimistic, whereas the Bayesian methods yield more credible capital and reinsurance payouts, particularly for the catastrophic layers. The proposed hazard blend offers a robust framework for actuaries, enhancing both methodological rigor and practical applicability in the composite loss modeling.
Abstract Telematics has emerged as one of the most critical data sources in today’s auto insurance industry. Despite the potential predictive value of telematics information for auto insurance claims, such data are typically available for only a small subset of policyholders, leaving the majority without telematics features. In this paper, we propose a multi-view ensemble learning framework to address this unique data structure. We consider multiple predictive models trained on different data views and combine these heterogeneous models through Bayesian model averaging. Through an extensive experimental study, we demonstrate that the proposed method assigns data-adaptive weights to individual models and delivers robust predictive performance across a variety of practical settings.
