How to Manage Inflation Risk in an Asset Allocation Problem : An Algebraic Approximated Solution

This paper analyses the portfolio problem of an investor who whants to maximize the expected utility of his terminal real wealth in an incomplete financial market. The investor must cope with a set of stochastic investment opportunities and inflation risk following a jump-diffusion process. We investigate how the inflation risk affects the optimal portfolio composition and, at this aim, we present an approximated analytical solution to the portfolio choice problem based on the Feynman-Kac representation theorem. Finally, we compare our approximated solution with some exact solutions available in the literature and we find that the main qualitative results are maintained.