Optimal Investment for Worst-Case Crash Scenarios: A Martingale Approach

Frank Thomas Seifried

34 citations0/0 files storedMathematics of Operations Research

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

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 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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1971Optimum consumption and portfolio rules in a continuous-time model 1985The equity premium: A puzzle 1969Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 2003Financial Modelling with Jump Processes 1989Recursive Methods in Economic Dynamics 1979Manias, Panics, and Crashes: A History of Financial Crises 2006Rare Disasters and Asset Markets in the Twentieth Century*1998Methods of Mathematical Finance

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