Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process

Abstract

In this paper, we investigate the pricing problem for a portfolio of life insurance contracts where the life contingent payments are equity-linked depending on the performance of a risky stock or index. The shot-noise effects are incorporated in the modeling of stock prices, implying that sudden jumps in the stock price are allowed, but their effects may gradually decline over time. The contracts are priced using the principle of equivalent utility. Under the assumption of exponential utility, we find the optimal investment strategy and show that the indifference premium solves a non-linear partial integro-differential equation (PIDE). The Feynman–Kač form solutions are derived for two special cases of the PIDE. We further discuss the problem for the asymptotic shot-noise process, and find the probabilistic representation of the indifference premium. We also provide some numerical examples and analyze parameter sensitivities for the results obtained in this paper.