## Abstract

We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogeneous portfolios. The density of the limiting measure is shown to solve a nonlinear stochastic partial differential equation, and certain moments of the limiting measure are shown to satisfy an infinite system of stochastic differential equations. The solution to this system leads to the distribution of the limiting portfolio loss, which we propose as an approximation to the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight its computational advantages over a direct Monte Carlo simulation of the original stochastic system.

Original language | English (US) |
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Pages (from-to) | 77-114 |

Number of pages | 38 |

Journal | Mathematical Finance |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2015 |

## Keywords

- Credit risk
- Interacting point process
- Law of large numbers

## ASJC Scopus subject areas

- Accounting
- Finance
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Applied Mathematics