TY - JOUR

T1 - Problems of ruin and survival in economics

T2 - applications of limit theorems in probability

AU - Bhattacharya, Rabi

AU - Majumdar, Mukul

AU - Lin, Lizhen

N1 - Funding Information:
*Research partially supported by NSF Grant DMS 1107053
Publisher Copyright:
© 2013, Indian Statistical Institute.

PY - 2013/11/1

Y1 - 2013/11/1

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.

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U2 - 10.1007/s13571-013-0068-1

DO - 10.1007/s13571-013-0068-1

M3 - Article

AN - SCOPUS:84893711263

VL - 75

SP - 145

EP - 180

JO - Sankhya B

JF - Sankhya B

SN - 0976-8386

IS - 2

ER -