Dynamic programming principle and computable prices in financial market models with transaction costs

TL;DR

This paper develops a dynamic programming approach to compute super-hedging costs in discrete-time financial markets with transaction costs, including complex models like order books and fixed costs.

Contribution

It introduces a dynamic programming principle applicable to a broad class of market models with various transaction cost structures.

Findings

Established a dynamic programming principle for super-hedging costs

Proved implementability under certain conditions on market processes

Applicable to convex and non-convex transaction cost models

Abstract

How to compute (super) hedging costs in rather general fi- nancial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it remains difficult to deduce numerical procedure to estimate them. We establish here a dynamic programming principle and we prove that it is possible to implement it under some conditions on the conditional supports of the price and volume processes for a large class of market models including convex costs such as order books but also non convex costs, e.g. fixed cost models.