Indifference pricing of pure endowments in a regime-switching market model

TL;DR

This paper develops a model for pricing pure endowments using indifference pricing in a regime-switching market, incorporating stochastic factors, jump-diffusions, and optimal investment strategies, with numerical analysis of parameter effects.

Contribution

It introduces a novel regime-switching model for indifference pricing of endowments, combining stochastic control, PDE characterization, and probabilistic representations.

Findings

Indifference prices are characterized by linear PDEs.

Optimal investment strategies are derived via Hamilton-Jacobi-Bellman equations.

Numerical experiments reveal parameter sensitivities and regime impacts.

Abstract

In this paper, we study the exponential utility indifference pricing of pure endowment policies within a stochastic-factor model for an insurer who also invests in a financial market. Our framework incorporates a hazard rate modeled as an observable diffusion process, while the risky asset price follows a jump-diffusion process driven by a continuous-time finite-state Markov chain, effectively capturing different economic regimes. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we derive optimal investment strategies with and without the insurance derivative and characterize the indifference price as a classical solution to a linear partial differential equation (PDE). Additionally, we provide a probabilistic representation of the indifference price via an extension of the Feynman-Kac formula and show that it satisfies a suitable backward PDE. Finally, some numerical experiments are conducted to perform sensitivity analyses, highlighting the impact of key model parameters.