scholarly journals On a Triplet of Exponential Brownian Functionals

2001 ◽  
pp. 396-415 ◽  
Author(s):  
Larbi Alili ◽  
Hiroyuki Matsumoto ◽  
Tomoyuki Shiraishi
Keyword(s):  
Exponential Brownian Functionals

Optimal importance sampling for the Laplace transform of exponential Brownian functionals

2016 ◽  
Vol 53 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Je Guk Kim
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Performance Analysis ◽  
Laplace Transform ◽  
Importance Sampling ◽  
Pricing Model ◽  
Asymptotically Optimal ◽  
Closed Form Solutions ◽  
The Laplace Transform ◽  
Exponential Brownian Functionals

Abstract We present an asymptotically optimal importance sampling for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals which plays a prominent role in many disciplines. To this end we utilize the theory of large deviations to reduce finding an asymptotically optimal importance sampling measure to solving a calculus of variations problem. Closed-form solutions are obtained. In addition we also present a path to the test of regularity of optimal drift which is an issue in implementing the proposed method. The performance analysis of the method is provided through the Dothan bond pricing model.

A DIRECT SOLUTION TO THE FOKKER–PLANCK EQUATION FOR EXPONENTIAL BROWNIAN FUNCTIONALS

2010 ◽  
Vol 08 (03) ◽  
pp. 287-304 ◽  
Author(s):  
CAROLINE PINTOUX ◽  
NICOLAS PRIVAULT
Keyword(s):  
Integral Representation ◽  
Gamma Function ◽  
Planck Equation ◽  
Heat Kernels ◽  
Direct Solution ◽  
Spectral Expansions ◽  
Fokker Planck Equation ◽  
Financial Application ◽  
Exponential Brownian Functionals ◽  
Fokker Planck

The solution of the Fokker–Planck equation for exponential Brownian functionals usually involves spectral expansions that are difficult to compute explicitly. In this paper, we propose a direct solution based on heat kernels and a new integral representation for the square modulus of the Gamma function. A financial application to bond pricing in the Dothan model is also presented.

scholarly journals Tree structured independence for exponential Brownian functionals

2009 ◽  
Vol 119 (10) ◽  
pp. 3798-3815 ◽  
Author(s):  
Hiroyuki Matsumoto ◽  
Jacek Wesołowski ◽  
Piotr Witkowski
Keyword(s):  
Exponential Brownian Functionals

Closed form modeling of evolutionary rates by exponential Brownian functionals

2015 ◽  
Vol 71 (6-7) ◽  
pp. 1387-1409 ◽  
Author(s):  
Nicolas Privault ◽  
Stéphane Guindon
Keyword(s):  
Closed Form ◽  
Evolutionary Rates ◽  
Exponential Brownian Functionals
Sign in / Sign up

Export Citation Format

Share Document