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

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.