Problems of ruin and survival in economics

Applications of limit theorems in probability

Rabindra N Bhattacharya, Mukul Majumdar, Lizhen Lin

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)145-180
Number of pages36
JournalSankhya: The Indian Journal of Statistics
Volume75 B
Issue numberPART 2
StatePublished - 2013

Fingerprint

Limit Theorems
Economics
Exchange Economy
Probability of Ruin
Markov Process
Mathematical Model
Resources
Computing
Limit theorems
Ruin
Model
Exchange economy
Markov process
Endowments
Mathematical model
Probability of ruin
Income
Exhaustion
Loans
Credit

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

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

In: Sankhya: The Indian Journal of Statistics, Vol. 75 B, No. PART 2, 2013, p. 145-180.

Research output: Contribution to journalArticle

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