Numerical methods for optimal insurance demand under marked point processes shocks

TL;DR

This paper develops a numerical method to determine optimal insurance strategies that minimize shocks in wealth processes modeled by marked point processes, using dual control and viscosity solutions.

Contribution

It introduces a numerical algorithm based on policy iterations to solve the Hamilton Jacobi Bellman Variational Inequality for optimal insurance under shock processes.

Findings

Effective numerical scheme for optimal insurance strategies.

Validation of the approach through convergence and stability analysis.

Application to complex shock models with marked point processes.

Abstract

This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the shocks. This optimization problem is related to a suitable dual stochastic control problem in which the delicate boundary constraints disappear. In Mnif \cite{mnif10}, the dual value function is characterized as the unique viscosity solution of the corresponding Hamilton Jacobi Bellman Variational Inequality (HJBVI in short). We characterize the optimal insurance strategy by the solution of the variational inequality which we solve numerically by using an algorithm based on policy iterations.