Discrete time shadow price revisited

TL;DR

This paper revisits the concept of discrete time shadow prices in markets with multiple assets and bid-ask spreads, providing methods to construct shadow prices for static and dynamic models.

Contribution

It introduces a new approach to constructing shadow prices for multiple assets in discrete time, extending previous work to dynamic models and multiple assets.

Findings

Constructed shadow prices for two-asset static models

Extended shadow price construction to dynamic models

Presented methods for multiple assets in discrete time

Abstract

In the paper discrete time shadow price is constructed for the market with several assets with given bid and ask prices. Shadow price is the price such that the problem of optimal utility from terminal wealth on the market without transaction costs gives the same value function as in the case of bid and ask prices. In the paper we solve first static problem for two assets and then we construct the shadow price for dynamic model. Finally we present construction of the shadow price for several assets.