Utility-based indifference pricing of pure endowments in a Markov-modulated market model

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.