OPTIMAL RISK CONTROL UNDER MARKED POINT PROCESSES SHOCKS: A DYNAMIC PROGRAMMING DUALITY APPROACH

We study the stochastic control problem of maximizing expected utility from terminal wealth under a nonbankruptcy constraint. The problem of the agent is to derive the optimal insurance strategy which reduces his exposure to the risk. This optimization problem is related to a suitable dual stochastic control problem in which the delicate boundary constraints disappear. We characterize the dual value function 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.