### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Finance
- Applied Mathematics

### Cite this

*SIAM Journal on Financial Mathematics*,

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

}

*SIAM Journal on Financial Mathematics*, vol. 8, no. 1, pp. 841-873. https://doi.org/10.1137/16M1095019

**A stochastic model of optimal debt management and bankruptcy.** / Bressan, Alberto; Marigonda, Antonio; Nguyen, Khai T.; Palladino, Michele.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A stochastic model of optimal debt management and bankruptcy

AU - Bressan, Alberto

AU - Marigonda, Antonio

AU - Nguyen, Khai T.

AU - Palladino, Michele

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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-.

AB - 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-.

UR - http://www.scopus.com/inward/record.url?scp=85041586490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041586490&partnerID=8YFLogxK

U2 - 10.1137/16M1095019

DO - 10.1137/16M1095019

M3 - Article

VL - 8

SP - 841

EP - 873

JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

SN - 1945-497X

IS - 1

ER -