Shadow price of information in discrete time stochastic optimization

TL;DR

This paper extends the concept of shadow prices of information in stochastic optimization, providing relaxed conditions for their existence and applications in financial mathematics and dynamic programming.

Contribution

It introduces a generalized framework allowing for unbounded decision strategies, ensuring solution existence and duality without traditional boundedness assumptions.

Findings

Established relaxed conditions for shadow price existence.

Derived dual forms of dynamic programming recursions.

Applied results to financial mathematics and integral functionals.

Abstract

The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and gives relaxed sufficient conditions for its existence. We allow for general adapted decision strategies, which enables one to establish the existence of solutions and the absence of a duality gap e.g. in various problems of financial mathematics where the usual boundedness assumptions fail. As applications, we calculate conjugates and subdifferentials of integral functionals and conditional expectations of normal integrands. We also give a dual form of the general dynamic programming recursion that characterizes shadow prices of information.