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In this paper, we take into account a very general setting with : (i) a set of stochastic investment opportunities, (ii) a set of risky assets, (iii) a riskless asset paying a stochastic interest rate, (iv) a stochastic inflation risk, (v) stochastic labor income , and (vi) HARA preferences. We compute a quasi-explicit solution for both the optimal consumption and asset allocation. This solution is based on two changes in the probability measure. We also show that the investor behaves as if he could rely on his wealth augmented by the expected value of all his “forward real labor incomes”

In this paper we take into account a very general setting with: (i)a set of stochastic investment opportunities, (ii) a set of risky assets, (iii) a riskless asset paying a stochastic interest rate, (iv) a stochastic inflation risk, (v) stochastic labor income, and (vi) HARA preferences. We compute a quasi-explicit solution for both the optimal consumption and asset allocation. This solution is based on two changes in the probability measure. We also show that the investor behaves as if he could rely on his wealth augmented by the expected value of all his ?forward real labor incomes?.

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.