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...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.展开更多
基金the German Science Foundation,Berlin Mathematical School and RTG 1845 for support,and Xiaolu Tan for helpful discussions.
文摘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.
