Utility maximization in a binomial model with transaction costs: a duality approach based on the shadow price process (Q2874727)

This paper deals with a expected utility maximization problem for a portfolio under proportional transaction costs and a long time horizon. The portfolio is made of two assets, one risk-free asset, which is assumed to be constant in time, and one stock. The utility considered here is the logarithmic function. The authors use a duality approach, based on shadow price processes, to derive asymptotic expansions of the size of the no-trade-region and the asymptotic growth rate in the binomial model. They find that the size of the no-trade-region as well as the asymptotic growth rate depend analytically on the level of transaction costs. This comes in contrast with what happens in the continuous time models case. Analytically, it is found that the Black-Scholes model appears as a singular limit of the family of binomial models. Consequently, the proposed methods for the binomial model cannot predict the results in the Black-Scholes model.NEWLINENEWLINEThe convergence of the no-trade-region and the asymptotic growth rate to the corresponding quantities in the Black-Scholes model was also investigated and compared with the convergence results obtained for the binomial model.