Good deal hedging and valuation under combined uncertainty about drift and volatility  

作　　者：Dirk Becherer Klebert Kentia 

机构地区：[1]Institut fur Mathematik,Humboldt Universitat,Unter den Linden 6,10099 Berlin,Germany [2]Institut fur Mathematik,Goethe-Universitat,D-60054 Frankfurt am Main,Germany

出　　处：《Probability, Uncertainty and Quantitative Risk》2017年第1期294-333,共40页概率、不确定性与定量风险（英文）

基　　金：the German Science Foundation,Berlin Mathematical School and RTG 1845 for support,and Xiaolu Tan for helpful discussions.

摘　　要：We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices.Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good,by restricting instantaneous Sharpe ratios.A non-dominated multiple priors approach to model uncertainty(ambiguity)leads to worst-case good-deal bounds.Corresponding hedging strategies arise as minimizers of a suitable coherent risk measure.Good-deal bounds and hedges for measurable claims are characterized by solutions to secondorder backward stochastic differential equations whose generators are non-convex in the volatility.These hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures,uniformly over all priors.

关 键 词：Combined drift and volatility uncertainty Good-deal bounds Robust hedging Hedging to acceptability Second-order BSDE Stochastic control 

分 类 号：O17[理学—数学]