Asymptotic analysis for optimal investment and consumption with transaction costs

Abstract

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,

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