Convergence of utility indifference prices to the superreplication price in a multiple-priors framework

TL;DR

This paper studies how utility indifference prices in a discrete-time market with model uncertainty converge to superreplication prices, extending classical results to a multiple-priors framework.

Contribution

It establishes the convergence of utility indifference prices to superreplication prices under non-dominated model uncertainty, a novel extension in the multiple-priors setting.

Findings

Utility indifference prices converge to superreplication prices under certain conditions.

Revisits and relates the certainty equivalent to absolute risk aversion for random utility functions.

Provides a theoretical foundation for pricing under model uncertainty.

Abstract

This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion.