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arXiv · 1609.05983

A Stochastic Model of Optimal Debt Management and Bankruptcy

Alberto Bressan·Antonio Marigonda·Khai T. Nguyen·Michele Palladino
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Abstract

A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size $x^*$, bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold $x^*$, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of $x^*$, changes, depending on different values of $x^*$?.

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Alberto Bressan, Antonio Marigonda, Khai T. Nguyen, Michele Palladino. 2016-09-20. A Stochastic Model of Optimal Debt Management and Bankruptcy. https://arxiv.org/abs/1609.05983

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