Optimal portfolio and background risk: an exact and an approximated solution

This paper analyses the portfolio problem of an investor maximizing the expected exponential utility of his terminal real wealth. The investor must cope with both a set of stochastic investment opportunities and a set of background risks. If the market is complete we are able to find an exact solution. If the market is incomplete, we suggest an approximated general solution. Contrary to other exact solutions obtained in the literature, all our results are obtained considering a stochastic inflation risk and without specifying any particular functional form for the stochastic variables involved in the problem.