Quantile Hedging in a Semi-Static Market with Model Uncertainty

TL;DR

This paper develops a method for quantile hedging in markets with model uncertainty, using discretization and duality to ensure existence and convergence of optimal strategies.

Contribution

It introduces a discretization approach for semi-static markets under model uncertainty, linking quantile hedging to hypothesis testing, and proves asymptotic optimality.

Findings

Discretized market has a dominating measure enabling numerical computation.

Approximate quantile hedging prices converge as discretization becomes finer.

Optimal hedging strategies are asymptotically optimal in the original market.

Abstract

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and helps numerical calculation of the quantile hedging price. As the discretization becomes finer, the approximate quantile hedging price converges and the hedging strategy is asymptotically optimal in the original market.