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Computing strategies for achieving acceptability: A Monte Carlo approach

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  • Pal, Soumik

Abstract

We consider a trader who wants to direct his or her portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a Monte Carlo algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy for achieving acceptability. We also prove optimality of the capital obtained. Explicit theoretical evaluations of hedging strategies are extremely difficult, and we avoid the problem by resorting to such computational methods. The main idea is to utilize the finite Vapnik-C[breve]ervonenkis dimension of a class of possible strategies.

Suggested Citation

  • Pal, Soumik, 2007. "Computing strategies for achieving acceptability: A Monte Carlo approach," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1587-1605, November.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:11:p:1587-1605
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    References listed on IDEAS

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    Cited by:

    1. Daniel Bartl & Ludovic Tangpi, 2020. "Non-asymptotic convergence rates for the plug-in estimation of risk measures," Papers 2003.10479, arXiv.org, revised Oct 2022.

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