Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Wednesday, November 18, 2020
Location:  Passcode: 790109 Virtual (4:00 PM to 5:00 PM)

Title:  Optimal Consumption under a Habit-Formation Constraint Based on Average Past Consumption

Abstract:   We consider an infinite horizon optimal consumption problem for an individual who forms consumption habit based on an exponentially weighted average of her past consumption rates. We assume that the individual seeks to maximize the expected discounted CRRA utility of her relative consumption-to-habit process, and that she is unwilling to consume at a rate that is below a certain proportion of her consumption habit. We consider two cases, one in which the individual invests only in a risk-free asset, and another scenario where she invests in a Black-Scholes market. In both cases, we find that there exists a threshold x* such that if the ratio of wealth-to-habit is above (respectively, below) x*, it is optimal to consume at a rate higher than (respectively, equal to) the minimum acceptable rate. Furthermore, the individual optimally consumes to attain specific wealth-to-habit and consumption-to-habit ratios. The optimal investment and consumption policies are obtained explicitly in terms of the solution of a nonlinear free-boundary problem, which we analyze in detail.


Speaker:  Bahman Angoshtari
Institution:  University of Miami

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