Jiaqin Wei Seminar
- Topic: Consumption-Investment Strategies with Non-Exponential Discounting
Jiaqin Wei, Postdoctoral Research Fellow, Department of Applied Finance and Actuarial Studies, Macquarie University
- Venue:E4A 623
- When: 8th August, 2014, (Fri)
- Time: 11am - 12pm (Morning Tea from 10.30am)
In this talk, I will revisit the consumption-investment problem with a general discount function in a non-Markovian framework. The coefficients in our model, including the interest rate, appreciation rate and volatility of the stock, are assumed to be adapted stochastic processes. This is a time-inconsistent control problem with random coefficients. Following Yong (2012a,b)'s method, first I study an N-person differential game. The martingale method is adopted to solve the optimization problem of each player and their optimal strategies and value functions can be characterized in terms of the unique solutions of some BSDEs. Then taking limit gives a time-consistent equilibrium consumption-investment strategy of the original problem. In the case with logarithmic utility function, the time-consistent equilibrium strategy consists of a deterministic function and the ratio of the market price of risk to the volatility, and the corresponding equilibrium value function can be characterized by the unique solution of a family of BSDEs parameterized by a time variable. In the case with power utility function, the time-consistent solutions is characterized by the solution of a new backward stochastic integral equation. The existence and uniqueness of the solution to this new equation is still left open.
This talk is based on two joint papers with Qian Zhao and Yang Shen.