Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs
Risk sensitive and risk neutral long run portfolio problems with consumption and proportional transaction costs are studied. Existence of solutions to suitable Bellman equations is shown. The asymptotics of the risk sensitive cost when the risk factor converges to $0$ is then considered. It turns out that optimal strategies are stationary functions of the portfolio (portions of the wealth invested in assets) and of economic factors. Furthermore an optimal portfolio strategy for a risk neutral control problem is nearly optimal for a risk sensitive portfolio cost functional with risk factor close to $0$.