The relations of Choquet Integral and G-Expectation

TL;DR

This paper demonstrates that in incomplete markets, Choquet expectation and minimax expectation are equivalent for pricing European options with monotone payoffs, linking these concepts through $g$-expectation and stochastic differential equations.

Contribution

It establishes the equivalence of Choquet and minimax expectations in option pricing, providing a new theoretical connection in financial mathematics.

Findings

Choquet and minimax expectations are equal for certain European options.

The result applies to payoffs that are monotone functions of the terminal stock price.

Links between $g$-expectation, stochastic differential equations, and option pricing are clarified.

Abstract

In incomplete financial markets, there exists a set of equivalent martingale measures (or risk-neutral probabilities) in an arbitrage-free pricing of the contingent claims. Minimax expectation is closely related to the $g$-expectation which is the solution of a certain stochastic differential equation. We show that Choquet expectation and minimax expectation are equal in pricing European type options, whose payoff is a monotone function of the terminal stock price $S_T$.