A note on pricing of contingent claims under G-expectation

TL;DR

This paper investigates the pricing of contingent claims considering volatility uncertainty using G-expectation, G-Brownian motion, and backward SDEs, providing explicit results in the Markovian case.

Contribution

It introduces a framework for pricing under G-expectation with volatility uncertainty, utilizing G-Brownian motion and backward SDEs, and derives explicit results for the Markovian case.

Findings

Superhedging and subhedging prices are obtained.

Explicit formulas derived for the Markovian case.

Framework accommodates volatility uncertainty in pricing.

Abstract

In this paper, we study the pricing of contingent claims under G-expectation. In order to accomodate volatility uncertainty, the price of the risky security is supposed to governed by a general linear stochastic differential equation (SDE) driven by G-Brownian motion. Utilizing the recently developed results of Backward SDE driven by G-Brownian motion, we obtain the superhedging and suberhedging prices of a given contingent claim. Explicit results in the Markovian case are also derived.