In this paper we investigate approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S | Lambda ] of S with respect to a conditioning random variable Lambda.The choice for Lambda is...

It is shown that the distribution of the ratio of two independent gamma-distributed random variables is infinitely divisible. This result provides a solution to an unsolved problem given by F. W. Steutel [4] in a survey of recent developments in the theory of infinite divisibility.

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process, and a shifted inverse Gaussian process to describe the logarithm of the stock...