Robust Consumption and Portfolio Policies When Asset Prices Can Jump

Abstract

We study the consumption-portfolio allocation problem in continuous time when asset prices follow Levy processes and the investor is concerned about potential model misspecification. We derive optimal consumption and portfolio policies that are robust to uncertainty about the hard-to-estimate drift rate, jump intensity and jump size parameters. We also provide a semi-closed form formula for the detection-error probability and compare various portfolio holding strategies, including robust and non-robust policies. Our quantitative analysis shows that ignoring uncertainty leads to significant wealth loss for the investor.