Construction of a shadow price for discrete infinite horizon discounted functionals
Volume 52 / 2025
Applicationes Mathematicae 52 (2025), 151-166
MSC: Primary 91G10; Secondary 91G15
DOI: 10.4064/am2576-10-2025
Published online: 3 November 2025
Abstract
We consider the problem of portfolio optimization for an infinite discrete time horizon under transaction costs. We study Bellman equations for this problem. The main goal of this article is to construct a shadow price, i.e. to prove the existence of an equivalent market without transaction costs for which the optimal strategy is the same as in the market with transaction costs.
