Title: Differential Game Models Of Optimal Debt Management
Speaker: Dr. Nguyễn Tiến Khải, Associate Professor, Department of Mathematics, North Carolina State University
Time: 9 AM, Sunday – 12 June 2022. Via Zoom. Meeting ID: 215 811 8519. Passcode: 879771
Abstract: I will present recent results on the game-theoretical formulation of optimal debt management problems in an infinite time horizon with exponential discount, modeled as a non-cooperative interaction between a borrower and a pool of risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a “solution” must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization processes”.