Blanchet JH, Sigman K. On exact sampling of stochastic perpetuities. Journal of Applied Probability. 2011;48(A):165-182. doi:10.1239/jap/1318940463
Abstract
A stochastic perpetuity takes the form D∞=∑n=0∞ exp(Y1+⋯+Yn)Bn, where Yn:n≥0) and (Bn:n≥0) are two independent sequences of independent and identically distributed random variables (RVs). This is an expression for the stationary distribution of the Markov chain defined recursively by Dn+1=AnDn+Bn, n≥0, where An=eYn; D∞ then satisfies the stochastic fixed-point equation D∞D̳AD∞+B, where A and B are independent copies of the An and Bn (and independent of D∞ on the right-hand side). In our framework, the quantity Bn, which represents a random reward at time n, is assumed to be positive, unbounded with EBnp 0, and have a suitably regular continuous positive density. The quantity Yn is assumed to be light tailed and represents a discount rate from time n to n-1. The RV D∞ then represents the net present value, in a stochastic economic environment, of an infinite stream of …
Authors
Jose H Blanchet, Karl Sigman
Publication date
2011/8
Journal
Journal of Applied Probability
Volume
48
Issue
A
Pages
165-182
Publisher
Cambridge University Press
