Optimal Multiple Stopping Problems under g-expectation

TL;DR

This paper investigates optimal multiple stopping problems under Knightian uncertainty using g-expectation, providing solutions for discrete and continuous cases with applications to swing option pricing.

Contribution

It introduces a new framework for multiple stopping under uncertainty via g-expectation and extends solutions to continuous-time cases with continuity results.

Findings

Discrete-time problem solved by induction method.

Continuous-time case requires continuity of reward family.

Application to swing option pricing in financial markets.

Abstract

In this paper, we study the optimal multiple stopping problem under Knightian uncertainty both under discrete-time case and continuous-time case. The Knightian uncertainty is modeled by a single real-valued function g, which is the generator of a kind of backward stochastic differential equations (BSDEs). We show that the value function of the multiple stopping problem coincides with the one corresponding to a new reward sequence or process. For the discrete-time case, this problem can be solved by an induction method which is a straightforward generalization of the single stopping theory. For the continuous-time case, we furthermore need to establish the continuity of the new reward family. This result can be applied to the pricing problem for swing options in financial markets, which give the holder of this contract at least two times rights to exercise it.