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

Dmitry Kramkov; Kim Weston

doi:10.1016/j.spa.2016.02.012

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arXiv · 1507.05865

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

Dmitry Kramkov·Kim Weston

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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.

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BibTeX RIS

Dmitry Kramkov, Kim Weston. 2015-07-21. Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure. https://doi.org/10.1016/j.spa.2016.02.012

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