On positive and negative moments of the integral of geometric Brownian motions
Let \(A_t(\mu)=\int_0^t\exp(2B_t+2\mu)dt\) where \(B\) is a standard Brownian motion. Recently, Dufresne obtained formulae for moments of this random variable involving the Gauss hypergeometric function. The note gives alternative proofs based on a distributional identity due to Matsumoto and Yor.
scientific article; zbMATH DE number 1506808
scientific article