Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs
SIAM Journal on Financial Mathematics, Forthcoming
26 Pages Posted: 4 Jan 2014
Date Written: January 2, 2014
Abstract
We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of her investment at the final time T, in the presence of a positive proportional transaction cost Λ>0. The utility function is of the form U(c)=c^{p}/p for p<1, and p no equal to zero. We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of Λ {1/3}. We also obtain a "nearly optimal" strategy, whose utility asymptotically matches the leading terms in the value function.
Keywords: Transaction costs, optimal control, asymptotic analysis, utility maximization
JEL Classification: G11
Suggested Citation: Suggested Citation