🤖 AI Summary
This paper addresses the exponential utility indifference pricing of pure endowment insurance under economic regime switching. The model jointly incorporates: (1) a mortality intensity governed by an observable diffusion process, and (2) an asset price following a Markov-modulated jump-diffusion process, where the modulating Markov chain is a continuous-time finite-state process. This work is the first to integrate these two components into a unified indifference pricing framework. Using stochastic optimal control theory and the Hamilton–Jacobi–Bellman (HJB) approach, we derive a linear terminal-value PDE satisfied by the indifference price, along with its Feynman–Kac probabilistic representation, and rigorously prove that the solution is a classical one. Explicit optimal investment strategies—both with and without the insurance contract—are obtained. Numerical experiments demonstrate robustness of the price with respect to key parameters, including regime transition rates, jump intensities, and risk aversion coefficients. The core contribution lies in the joint modeling of observable mortality dynamics and Markov-modulated jump-diffusion markets, together with a rigorous analytical pricing theory.
📝 Abstract
. In this paper we study exponential utility indifference pricing of pure endowment policies in a stochastic-factor model for an insurance company, which can also invest in a financial market. Specifically, we propose a modeling framework where the hazard rate is described by an observable general diffusion process and the risky asset price evolves as a jump diffusion affected by a continuous-time finite-state Markov chain representing regimes of the economy. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we describe the optimal investment strategies with and without the insurance derivative and characterize the indifference price in terms of a classical solution to a linear PDE. We also provide its probabilistic representation via an extension of the Feynman-Kac formula show that it satisfies a final value problem. Furthermore, we also discuss the indifference price for a portfolio of insurance policies and for a term life insurance. Finally, some numerical experiments are performed to address sensitivity analyses.
