We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost $\lambda > 0$ . The utility function is of the form U(c)=c 1-p /(1-p) for p > 0, $p\neq 1$ . We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of $\lambda^{1/3}$ , and we also obtain asymptotic results on the boundary of the “no-trade” region. Copyright Springer-Verlag Berlin/Heidelberg 2004Transaction costs, optimal control, asymptotic analysis, utility maximation,

We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge-fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic control problem is solved using dynamic programming arguments. We show by analytical methods that the associated Hamilton-Jacobi-Bellman equation has a smooth solution, and then obtain the existence and representation of the optimal control in feedback form using verification arguments.

No abstract

No abstract

No abstract