On the stochastic equation L(X)=L[B(X+C)] and a property of gamma distributions
Dufresne, Daniel
Bernoulli, Tome 2 (1996) no. 3, p. 287-291 / Harvested from Project Euclid
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This paper is concerned with the stochastic equation X = B(X+C), where B, X and C are independent. This equation has appeared in a number of contexts, notably in actuarial science. An apparently new property of gamma variables (Theorem 1) leads to the derivation of a new explicit example of solution of the stochastic equation (Theorem 2), where B is the product of two independent beta variables, C is gamma and X is the product of independent beta and gamma variables. Also, a number of previously known explicit examples are seen to be direct algebraic consequences of a well-known property of gamma variables.
Publié le : 1996-09-14
Classification:  discounted sums,  gamma variables,  hypergeometric functions 
@article{1178291724,
     author = {Dufresne, Daniel},
     title = {On the stochastic equation L(X)=L[B(X+C)] and a property of gamma distributions},
     journal = {Bernoulli},
     volume = {2},
     number = {3},
     year = {1996},
     pages = { 287-291},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178291724}
}

Dufresne, Daniel. On the stochastic equation L(X)=L[B(X+C)] and a property of gamma distributions. Bernoulli, Tome 2 (1996) no. 3, pp.  287-291. http://gdmltest.u-ga.fr/item/1178291724/