Asset pricing under model uncertainty with discrete time and states

TL;DR

This paper develops a framework for asset pricing under model uncertainty in discrete time and states, introducing new arbitrage definitions and extending results to multi-period models with superhedging prices.

Contribution

It provides a novel arbitrage definition under multiple probability measures and extends single-period results to multi-period models with superhedging prices.

Findings

Established necessary and sufficient conditions for no-arbitrage under model uncertainty.

Connected arbitrage concepts with risk-neutral measures in a multi-probability setting.

Derived superhedging prices for contingent claims under model uncertainty.

Abstract

In this study, we consider the asset pricing under model uncertainty with discrete time and states structure. For the single-period securities model, we give a novel definition of arbitrage under a family of probability, and explore of its relationship with risk neutral probability measure. Focusing on the financial market with short sales prohibitions, we separately investigate the necessary and sufficient conditions for no-arbitrage asset pricing based on nonlinear expectation which composed with a family of probability. When each linear expectation driven by the probability in the family of probability becomes a martingale measure, the necessary and sufficient conditions are same, which coincide with the existing results. Furthermore, we expand the main results of single-period securities model to the case of multi-period securities model. By-product, we obtain the superhedging prices of contingent claim under model uncertainty.