Quantile Hedging in a semi-static market with model uncertainty
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.
KeywordsQuantile hedging Model uncertainty Semi-static hedging Neyman–Pearson Lemma
- Bertsekas DP, Shreve SE (1978) Stochastic optimal control: the discrete time case, vol. 139 of mathematics in science and engineering. Academic Press, New YorkGoogle Scholar
- Dynkin EB, Yushkevich AA (1979) Controlled Markov processes, vol. 235 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin-New York, 1979. Translated from the Russian original by J. M. Danskin and C. HollandGoogle Scholar
- Grant M, Boyd S (2014) CVX: Matlab software for disciplined convex programming, version 2.1Google Scholar