Keywords: convex duality, duality gap, equivalent martingale measures, HARA utility functions, HJB equation, incomplete markets, Poisson processes, portfolio optimisation, risky assets, risk-aversion coefficient, hyperbolic absolute risk aversion, terminal wealth, financial risk
Optimal portfolio for HARA utility functions in a pure jump multidimensional incomplete market
In this paper, we analyse a pure jump incomplete market where the risky assets can jump upwards or downwards. In this market we show that, when an investor wants to maximise a HARA utility function of his/her terminal wealth, his/her optimal strategy consists of keeping constant proportions of wealth in the risky assets, thus extending the classical Merton result to this market. Finally, we compare our results with the classical ones in the diffusion case in terms of scalar dependence of portfolio proportions on the risk-aversion coefficient.