Optimal Payments to Connected Depositors in Turbulent Times - A Markov Chain Approach

28 Pages Posted: 27 May 2016

See all articles by Dávid Csercsik

Dávid Csercsik

Peter Pazmany Catholic University

Hubert Janos Kiss

Eötvös Loránd University; Hungarian Academy of Sciences (HAS) - Institute of Economics CERS-HAS (IEHAS)

Date Written: May 26, 2016

Abstract

We propose a discrete time probabilistic model of depositor behavior which takes into account the information flow among depositors. In each time period each depositors’ current state is determined in a stochastic way, based on its previous state, the state of other connected depositors and the strategy of the bank. The bank offers payment to impatient depositors who accept or decline them with certain probability, depending on the offered amount. The connections between depositors affect the evolution of the state trajectory as well: the more other connected depositors demand money from the bank, the larger is the probability that the depositor turns also impatient. Our principal aim is to see how are the optimal offers of the bank if it wants to keep the expected chance of a bank run under a certain level and minimize its expected payments, while taking into account the connection structure of the depositors. We show that in the case of the proposed model this question results in a nonlinear optimization problem with nonlinear constraints, and that the method is capable of accounting for time-varying resource limits of the bank. Optimal offers increase a) in the degree of the depositor; b) in the probability of being hit by a liquidity shock, and c) the effect of a neighboring impatient depositor.

Keywords: Bank runs, Markov chains, Network, Optimization

JEL Classification: C61, C63, G21

Suggested Citation

Csercsik, Dávid and Kiss, Hubert Janos, Optimal Payments to Connected Depositors in Turbulent Times - A Markov Chain Approach (May 26, 2016). Available at SSRN: https://ssrn.com/abstract=2784692 or http://dx.doi.org/10.2139/ssrn.2784692

Dávid Csercsik

Peter Pazmany Catholic University ( email )

Szentkirályi utca 28
Budapest
Hungary

Hubert Janos Kiss (Contact Author)

Eötvös Loránd University ( email )

Pazmany Peter setany 1A
Budapest, -- H1117
Hungary

Hungarian Academy of Sciences (HAS) - Institute of Economics CERS-HAS (IEHAS) ( email )

Budaorsi ut 45
Budapest, 1112
Hungary

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