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.
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Research partially supported by NSF Grant DMS 1107053.
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Bhattacharya, R., Majumdar, M. & Lin, L. Problems of ruin and survival in economics: applications of limit theorems in probability. Sankhya B 75, 145–180 (2013). https://doi.org/10.1007/s13571-013-0068-1
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DOI: https://doi.org/10.1007/s13571-013-0068-1
Keywords and phrases
- Collapse of credit system
- survival under Walrasian equilibrium
- renewable resource management
- large deviations
- CLT
- Lindley process