Abstract:

 In this article, we mainly discuss the optimal amount of investment for risky assets in stochastic hyperbolic discounting, assuming that investors’ consumption behavior is a Brownian motion. Based on the Hamilton-Jacobi-Bellman equation, the optimal investment portfolio with the constant absolute risk aversion investor is calculated, and the approximate solution of equation is given. Moreover, we analyzed some important properties of risky asset investment when consumption obeys the Wiener process, and then studied the relationship between consumption behavior and risky asset investment behavior.

Key words:

hyperbolic discounting, stochastic process, portfolio