Optimal Investment-consumption-insurance strategy with inflation risk and stochastic income in an Ito-levy setting

Abstract

In this study, we focus on finding the possible optimal strategy where there is consump tion, stochastic income, purchasing of life insurance and investment in risky and risk-less investments are made. The stock follows a jump diffusion process and the bond is linked to inflation making the two risky and we have the investment position taken also on the money market account. The wealth process is determined by the different generations of the life of an investor, that is before the investor dies and after the investor dies. We also look into the optimal portfolio the beneficiaries benefit after the investor dies. We applied the concept of change of probability measures considering the Girsanov’s and the Radon-Nikodym the orems, we found the generator of the Backward Stochastic differential equations defined and employed the Hamilton-Jacobi-Bellman dynamic programming (HJB) in finding the stochastic optimal controls of interest. The optimal strategies are explicitly obtained.