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

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  • Kramkov, Dmitry
  • Weston, Kim

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.

Suggested Citation

  • Kramkov, Dmitry & Weston, Kim, 2016. "Muckenhoupt’s (Ap) condition and the existence of the optimal martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2615-2633.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2615-2633
    DOI: 10.1016/j.spa.2016.02.012
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    References listed on IDEAS

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    Cited by:

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    2. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2020. "Conditional Davis pricing," Finance and Stochastics, Springer, vol. 24(3), pages 565-599, July.

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