In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 48, No. A ( 2011-08), p. 165-182
Abstract:
A stochastic perpetuity takes the form D ∞=∑ n =0 ∞ exp( Y 1 +⋯+ Y n ) B n , where Y n : n ≥0) and ( B n : 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 D n +1 = A n D n + B n , n ≥0, where A n =e Y n ; D ∞ then satisfies the stochastic fixed-point equation D ∞ D̳ AD ∞ + B , where A and B are independent copies of the A n and B n (and independent of D ∞ on the right-hand side). In our framework, the quantity B n , which represents a random reward at time n , is assumed to be positive, unbounded with E B n p 〈 ∞ for some p 〉 0, and have a suitably regular continuous positive density. The quantity Y n 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 stochastic rewards. We provide an exact simulation algorithm for generating samples of D ∞ . Our method is a variation of dominated coupling from the past and it involves constructing a sequence of dominating processes.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
DOI:
10.1239/jap/1318940463
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2011
detail.hit.zdb_id:
219147-7
detail.hit.zdb_id:
1474599-9
SSG:
3,2
