Muckenhoupt’s (Ap) condition and the existence of the optimal martingale measure

Dmitry Kramkov and Kim Weston

Stochastic Processes and their Applications, 2016, vol. 126, issue 9, 2615-2633

Abstract: In the problem of optimal investment with a utility function defined on (0,∞), we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt (Ap) condition for the power p=1/(1−a), where a∈(0,1) is a lower bound on the relative risk-aversion of the utility function. We construct a counterexample showing that this (Ap) condition is sharp.

Keywords: Utility maximization; Optimal martingale measure; BMO martingales; (Ap) condition (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:9:p:2615-2633

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DOI: 10.1016/j.spa.2016.02.012

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