Optimal investment–consumption–insurance strategy with inflation risk and stochastic income in an Itô–Lévy setting

Abstract

This paper’s focus is on finding the optimal strategies for a trader who invests in stock, a money market account and an inflation-linked index bond. The stock follows a jump diffusion process and the bond is linked to inflation making the two risky. The optimal strategies are determined on two generations of the life of an investor, that is before the investor dies and after the investor dies. We applied the concept of change of probability measures considering Girsanov’s and the Radon–Nikodym theorems. We found the generator of the Backward Stochastic differential equations defined and employed the Hamilton–Jacobi–Bellman (HJB) dynamic programming in finding the stochastic optimal controls of interest.