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arXiv · 2301.13575

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

Alessandra Cretarola·Benedetta Salterini
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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.

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Alessandra Cretarola, Benedetta Salterini. 2023-01-31. Indifference pricing of pure endowments in a regime-switching market model. https://arxiv.org/abs/2301.13575

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