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

Abstract

This paper formulates a utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. Investor preferences are described by possibly random utility functions defined on the positive axis. We prove that when the investors's absolute risk aversion tends to infinity, 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 multiple‐priors and establish its relation with risk aversion.

Utility maximization with proportional transaction costs under model uncertainty

“…The next result shows the risk-averse asymptotics on the utility indifference prices. Similar results can also be found in [21,13,3]. Proposition 3.6.…”

“…Analogous to the dominated case, the pricing-hedging duality can usually be obtained by studying the superhedging problem under some appropriate no-arbitrage conditions. The non-dominated robust utility maximization in the discrete time frictionless market was first examined by [31], where the dynamic programming principle plays the major role to derive the existence of the optimal primal strategy without passing to the dual problem, see some further extensions in [30,12,13]. In a context where the model uncertainty is represented by a collection of stochastic processes, [33] proved the existence of the optimal strategy for the utility function defined either over the positive or over the whole real line.…”