  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.
