### Abstract

In this paper the focus is on characterizing and computing the probabilities of ruin in three mathematical models arising in economics. First, we examine a credit system in which small loans without collaterals are extended to a large number of costumers, and study the probability of collapse due to defaults. Next, we consider a Walrasian model of an exchange economy in which the endowments are random, and analyze the probability that at equilibrium prices an agent does not have the minimum income needed for survival. Finally, the problem of sustaining a constant consumption of a resource the stock of which is augmented by a random input is considered. The steady state of the resulting Markov process, the speed at which it is approached, and the possibility of exhaustion of the stock are examined.

Original language | English (US) |
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Pages (from-to) | 145-180 |

Number of pages | 36 |

Journal | Sankhya: The Indian Journal of Statistics |

Volume | 75 B |

Issue number | PART 2 |

State | Published - Dec 1 2013 |

### Keywords

- Clt
- Collapse of credit system
- Large deviations
- Lindley process
- Renewable resource management
- Survival under walrasian equilibrium

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Sankhya: The Indian Journal of Statistics*,

*75 B*(PART 2), 145-180.