### Abstract

A problem of optimal debt management is modeled as a noncooperative interaction between a borrower and a pool of lenders, in an 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 difierent values of x-.

Original language | English (US) |
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Pages (from-to) | 841-873 |

Number of pages | 33 |

Journal | SIAM Journal on Financial Mathematics |

Volume | 8 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Finance
- Applied Mathematics

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## Cite this

*SIAM Journal on Financial Mathematics*,

*8*(1), 841-873. https://doi.org/10.1137/16M1095019