Dynamic utility-based good deal bounds

Summary

We introduce and study no-good-deal valuation bounds defined in terms of expected utility. A utility-based good deal is a payoff whose expected utility is too high in comparison to the utility of its price. Forbidding good deals induces, via duality, restrictions on pricing kernels and thereby gives tighter valuation bounds on payoffs than absence of arbitrage alone. Our approach extends earlier work by Černý (2003) in several directions: We give rigorous results for a general probability space instead of finite Ω; we systematically use duality results to provide a streamlined approach with simple arguments; we do all this rigorously for both static and dynamic situations; and we give a systematic comparison between local and global (conditional) pricing kernel restrictions for the temporally dynamic setting. For the dynamic case, we show in a Lévy framework that defining no-good-deal valuation measures by imposing local conditional restrictions on their instantaneous market prices of risk gives valuation bounds having very good dynamic properties as processes over time. We also show that global restrictions cannot yield such results in general.