Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure

Dmitry Kramkov and Kim Weston

Papers from arXiv.org

Abstract: In the problem of optimal investment with utility function defined on $(0,\infty)$, 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 $(A_p)$ condition for the power $p=1/(1-a)$, where $a\in (0,1)$ is a lower bound on the relative risk-aversion of the utility function. We construct a counterexample showing that this $(A_p)$ condition is sharp.

Date: 2015-07
New Economics Papers: this item is included in nep-upt
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Published in Stochastic Processes and their Applications, 126(9), 2016, p. 2615-2633

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