The Institute for Statistics and Mathematics (Department of Finance, Accounting and Statistics) cordially invites everyone interested to attend the talks in our Research Seminar Series, where internationally renowned scholars from leading universities present and discuss their (working) papers.

The list of talks for the summer term 2018 is available via the following link: <link en statmath resseminar>Summer Term 2018

Abstract:
Evaluating cumulative distribution function (CDF) and probability density function (PDF) of the sum of lognormal random variates by Monte Carlo simulation is a topic discussed in several recent papers. Our experiments show, that in particular for variances smaller than one, conditional Monte Carlo (CMC) in a well chosen main direction leads already to a quite simple algorithm with large variance reduction.
For the general case the implementation of the CMC algorithm requires numeric root finding which can be implemented robustly using upper and lower bounds for the root. Adding importance sampling (IS) to the CMC algorithm can lead to large additional variance reduction. For the special case of independent and identically distributed (IID) lognormal random variates the root is obtained in closed form. It is important that for this case the optimal importance sampling density is very close to the product of its conditional densities. So the product of the approximate one-dimensional conditional densities is used as multivariate IS density.
Applying the different approximation methods for the one-dimensional conditional densities, it is possible to obtain a significant additional variance reduction over the pure CMC algorithm by means of importance sampling. When also the density of the lognormal sum is required, it is important that an approximating function with continuous first derivative is available.
In this talk the variance reduction factors obtained with different approximation methods and the necessary setup times for the random variate generation algorithm are compared. Also the influence of the selected main direction is analyzed.

http://www.wu.ac.at/en/statmath/resseminar