Dynamic utility-based good deal bounds

Abstract

We introduce and study no-good-deal valuation bounds deflned in terms of ex- pected utility. A utility-based good deal is a payofi 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 payofis than absence of arbitrage alone. Our approach extends earlier work by • Cern¶ (2003) in several directions: We give rigorous results for a general proba- bility space instead of flnite ›; 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 Levy framework that deflning no- good-deal valuation measures by imposing local conditional restrictions on their instantaneous market prices of risk gives valuation bounds having very good dy- namic properties as processes over time. We also show that global restrictions cannot yield such results in general.