A worst-case approach for interest rate stresses and stock crashes

Abstract

Abstract In the current low interest rate environment even sovereign bonds cannot be considered as risk-free investments. To care for this aspect we introduce a worst-case continuous-time portfolio problem with combined stresses, that is, both stocks and the money market account can experience shocks in the form of unpredictable downward jumps in their values. We characterize the worst-case optimal portfolio strategy as an indifference strategy that is the solution of a constrained optimization problem. Our results generalize existing results in a multi-asset setting. Numerical examples demonstrate new effects in the presence of interest rate shocks. These insights can be used for risk management in the presence of crash risks.