Extend pricing to markets with non-unique equivalent martingale measures via a class of utility functions

Develop an extension of the proposed data-driven option pricing methodology to the case where the equivalent martingale measure is not unique by employing a class of utility functions (beyond logarithmic utility) in order to determine an interval of no-arbitrage prices for contingent claims.

Background

The paper’s methodology recovers a pricing kernel by solving a logarithmic utility maximization problem, which relies on the assumption that the risk-neutral measure is unique (market completeness). Under this assumption, the derivative price is unique and can be computed as the discounted expectation of its payoff under the risk-neutral measure.

The authors note that when uniqueness of the equivalent martingale measure fails, multiple no-arbitrage prices may exist. They suggest that, in such cases, one could consider a class of utility functions instead of only the logarithmic utility to obtain an interval of no-arbitrage prices, and explicitly note that this is left for future research.