Title: Worst-Case Optimal Investment in Incomplete Markets
Abstract: We study and solve the worst-case optimal portfolio problem of an investor with logarithmic preferences facing the possibility of a market crash.
Our setting takes place in a Lévy-market and we assume stochastic market coefficients. To tackle this problem, we enhance the martingale approach developed by F. Seifried in 2010. A utility crash-exposure transformation into a backward stochastic differential equation (BSDE) setting allows us to characterize the optimal indifference strategies.
Further, we deal with the question of existence of those indifference strategies
for market models with an unbounded market price of risk. To numerically compute the strategies, we solve the corresponding (non-Lipschitz) BSDEs through their associated PDEs and need to analyze continuity and boundedness properties of Cox-Ingersoll-Ross (CIR) forward processes.
We demonstrate our approach for Heston's stochastic volatility model, Bates' stochastic volatility model including jumps, and Kim-Omberg’s model for a stochastic excess
return.
