Robust hedging in incomplete markets

Abstract

AbstractWe considered a pension fund that needs to hedge uncertain long-term liabilities. We modeled the pension fund as a robust investor facing an incomplete market and fearing model uncertainty for the evolution of its liabilities. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst-case scenario by means of solving a min–max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy.