In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein–Uhlenbeck diffusion process, we compute the optimal portfolio strategy and the corresponding value. Our method of solution relies on duality, and it is purely probabilistic.

The geometric structure of the nonparametric statistical model of all positive densities connected by an open exponential arc and its intimate relation to Orlicz spaces give new insights to well-known financial objects which arise in exponential utility maximization problems.

We study an asset allocation problem for a defined-contribution (DC) pension scheme in its accumulation phase. We assume that the amount contributed to the pension fund by a pension plan member is coupled with the salary income which fluctuates randomly over time and contains both a hedgeable and non-hedgeable risk component. We consider an economy in which macroeconomic risks are existent. We assume that the economy can be in one of I states (regimes) and switches randomly between those states. The state of the economy affects the dynamics of the tradeable risky asset and the contribution process (the salary income of a pension plan member). To model the switching behavior of the economy we use a counting process with stochastic intensities. We find the investment strategy which maximizes the expected exponential utility of the discounted excess wealth over a target payment, e.g. a target lifetime annuity.