Closed-form expressions for the steady-state wealth distribution in a kinetic model of gambling

Abstract

We have successfully formulated a gamma-like closed-form expression for the steady-state wealth distribution in a kinetic model of gambling from a finite number of its moments as generated from a recursion relation derived from an arbitrary exchange distribution which is normalized in the interval (0,1). The obtained steady-state wealth distribution functions are qualitatively similar with those existing in literature. We have shown the utility of our proposed model by the ability to easily calibrate the parameters in the model to accurately represent wealth distributions existing in real economies.