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This paper analyses the portfolio problem of an investor who wants to maximize the expected exponential utility of his terminal wealth both in a complete and an incomplete financial market. The investor must cope with a set of stochastic investment opportunities and two sets of background risks. If the market is complete we are able to find an exact solution. Instead, 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 without specifying any particular functional form for the stochastic variables involved in the problem.JEL classification: G11, C61.

We solve a mean-variance optimisation problem in the accumulation phase of a defined contribution pension scheme. In a general multi-asset financial market with stochastic investment opportunities and stochastic contributions, we provide the general forms for the efficient frontier, the optimal investment strategy, and the ruin probability. We show that the mean-variance approach is equivalent to a "userfriendly" target-based optimisation problem which minimises a quadratic loss function, and provide implementation guidelines for the selection of the target. We show that the ruin probability can be kept under control through the choice of the target level. We find closed-form solutions for the special case of stochastic interest rate following the Vasiček (1977) dynamics, contributions following a geometric Brownian motion, and market consisting of cash, one bond and one stock. Numerical applications report the behaviour over time of optimal strategies and non-negative constrained strategies.