  We discuss an optimal investment, consumption and insurance problem of a wage
earner under inflation. Assume a wage earner investing in a real money account
and three asset prices, namely: a real zero coupon bond, the inflation-linked
real money account and a risky share described by jump-diffusion processes.
Using the theory of quadratic-exponential backward stochastic differential
equation (BSDE) with jumps approach, we derive the optimal strategy for the two
typical utilities (exponential and power) and the value function is
characterized as a solution of BSDE with jumps. Finally, we derive the explicit
solutions for the optimal investment in both cases of exponential and power
utility functions for a diffusion case.
