Asymptotic analysis for optimal investment and consumption with transaction costs

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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\lambda > 0$</EquationSource> </InlineEquation>. The utility function is of the form U(c)=c <Superscript>1-p </Superscript>/(1-p) for p > 0, <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$p\neq 1$</EquationSource> </InlineEquation>. We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\lambda^{1/3}$</EquationSource> </InlineEquation>, and we also obtain asymptotic results on the boundary of the “no-trade” region. Copyright Springer-Verlag Berlin/Heidelberg 2004