Stochastic representation under g-expectation and applications: the discrete time case

TL;DR

This paper explores stochastic representation under g-expectation in discrete time, establishing foundational results and applying them to optimal stopping, American option pricing under uncertainty, and obstacle problems.

Contribution

It provides the first comprehensive analysis of stochastic representation under g-expectation in discrete time, including existence, uniqueness, and characterization of solutions.

Findings

Established existence and uniqueness of solutions under g-expectation.

Developed a new approach to optimal stopping and American option pricing under uncertainty.

Applied results to non-linear Skorokhod-type obstacle problems.

Abstract

In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping problem under g-expectation and the related pricing of American options under Knightian uncertainty. Our results are also applied to a (non-linear) Skorokhod-type obstacle problem.