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

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 - 2013 |

### Fingerprint

### 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

### Cite this

*Sankhya: The Indian Journal of Statistics*,

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

**Problems of ruin and survival in economics : Applications of limit theorems in probability.** / Bhattacharya, Rabindra N; Majumdar, Mukul; Lin, Lizhen.

Research output: Contribution to journal › Article

*Sankhya: The Indian Journal of Statistics*, vol. 75 B, no. PART 2, pp. 145-180.

}

TY - JOUR

T1 - Problems of ruin and survival in economics

T2 - Applications of limit theorems in probability

AU - Bhattacharya, Rabindra N

AU - Majumdar, Mukul

AU - Lin, Lizhen

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Clt

KW - Collapse of credit system

KW - Large deviations

KW - Lindley process

KW - Renewable resource management

KW - Survival under walrasian equilibrium

UR - http://www.scopus.com/inward/record.url?scp=84893704838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893704838&partnerID=8YFLogxK

M3 - Article

VL - 75 B

SP - 145

EP - 180

JO - Sankhya: The Indian Journal of Statistics

JF - Sankhya: The Indian Journal of Statistics

SN - 0972-7671

IS - PART 2

ER -