Transaction Costs and Shadow Prices in Discrete Time

Transaction Costs and Shadow Prices in Discrete Time

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even in seemingly perfectly benign situations, i.e., for a log-investor trading in an...

On using shadow prices in portfolio optimization with transaction costs

In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676–713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, h...

Shadow Prices and Well-Posedness in the Problem of Optimal Investment and Consumption with Transaction Costs

On the Existence of Shadow Prices in Finite Discrete Time

A shadow price is a process S̃ lying within the bid/ask prices S, S of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process S̃ leads to the same maximal utility as in the original market with transaction costs. For finite Ω, this note provides an elementary proof for the existence of such a shadow price.

Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrari...