Optimal investment for worst-case crash scenarios: A martingale approach

Optimal investment for worst-case crash scenarios: A martingale approach

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Article ID: iaor20106291
Volume: 35
Issue: 3
Start Page Number: 559
End Page Number: 579
Publication Date: Aug 2010
Journal: Mathematics of Operations Research
Authors:
Keywords: portfolio management
Abstract:

We investigate the optimal portfolio problem under the threat of a financial market crash in a multidimensional jump-diffusion framework. We set up a nonprobabilistic crash model and consider an investor that seeks to maximize Constant Relative Risk Aversion (CRRA) utility in the worst possible crash scenario. We recast the problem as a stochastic differential game; with the help of the fundamental notion of indifference strategies, we completely solve the portfolio problem using martingale arguments.

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