Dynamic safety first expected utility model

Levy and Levy (2009) empirically show that a combination of safety first and expected utility (SFEU) principles play a key role in human decision-making process. This paper extends the SFEU model to the optimal dynamic investment in a continuous-time economy. We derive the analytic optimal trading strategy using the martingale approach. Interestingly, the optimal trading strategy replicates a portfolio of a vanilla call, a vanilla put, a digital put option, and a cash reserve. These derivatives therefore match the objective of SFEU investors, which offers an explanation to their popularity in the market. The model also implies that investors with more awareness of crash risk demand put options with lower strike price. Using option data of US major market indices and alternative proxies for market awareness of crash risk, we empirically test the model implications and find that market awareness of crash risk can explain the dynamics of index option open interest.