On the Laplace Transform of the Lognormal Distribution

摘要: Integral transforms of the lognormal distribution are great importance in statis- tics and probability, yet closed-form expressions do not exist. A wide variety methods have been employed to provide approximations, both analytical numerical. In this paper, we analyse a approximation � L(θ ) Laplace transform which is obtained via modified version Laplace's method. This approximation, given terms Lambert W (·) function, tractable enough for applications. We prove that asymptotically equivalent as θ →∞ . apply result construct reliable Monte Carlo estimator it be logarithmically efficient rare event sense