Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach

摘要

We discuss an optimal investment, consumption and insurance problem of a wageearner under inflation. Assume a wage earner investing in a real money accountand three asset prices, namely: a real zero coupon bond, the inflation-linkedreal money account and a risky share described by jump-diffusion processes.Using the theory of quadratic-exponential backward stochastic differentialequation (BSDE) with jumps approach, we derive the optimal strategy for the twotypical utilities (exponential and power) and the value function ischaracterized as a solution of BSDE with jumps. Finally, we derive the explicitsolutions for the optimal investment in both cases of exponential and powerutility functions for a diffusion case.