Optimal long term growth rate of expected utility of wealth (Q1578591)

Using the technique of dynamic programming, the paper analyses in detail investment policies which result in optimal long term growth of expected utility of wealth under the following assumptions: The portfolio consists of one risky and one riskless asset and no transaction costs are considered; The price of stock is logarithmic Brownian motion with a constant volatility and a linear deterministic drift, i.e., Ornstein-Uhlenbeck type of model; HARA utility function with exponent \(\infty< \gamma<1\) is used. Both the unconstrained control (the fraction of wealth invested in the risky asset) and control limited to a finite interval or to \([0,+\infty)\) are considered. Interesting differences come out for positive values of \(\gamma\), for \(\gamma\to 0\) and for \(\gamma<0\). In the last case, it turns out that values of \(\gamma\geq -3\) and those smaller than \(-3\) have to be distinguished.