Affiliation:
1. Dipartimento di Matematica , Università di Roma “Tor Vergata” , Via della Ricerca Scientifica, 00133 Roma , Italy
Abstract
Abstract
We consider the problem of selecting a change of mean which minimizes the variance of Monte Carlo estimators for the expectation of a functional of a continuous Gaussian field, in particular
continuous Gaussian processes.
Functionals of Gaussian fields have taken up an important position in many fields
including statistical physics of disordered systems and mathematical finance
(see, for example,
[A. Comtet, C. Monthus and M. Yor,
Exponential functionals of Brownian motion and disordered systems,
J. Appl. Probab. 35 1998, 2, 255–271],
[D. Dufresne,
The integral of geometric Brownian motion,
Adv. in Appl. Probab. 33 2001, 1, 223–241],
[N. Privault and W. I. Uy,
Monte Carlo computation of the Laplace transform of exponential Brownian functionals,
Methodol. Comput. Appl. Probab. 15 2013, 3, 511–524] and
[V. R. Fatalov,
On the Laplace method for Gaussian measures in a Banach space,
Theory Probab. Appl. 58 2014, 2, 216–241].
Naturally, the problem of computing the expectation of such functionals, for example the Laplace transform,
is an important issue in such fields.
Some examples are considered, which, for particular Gaussian processes, can be related to option pricing.
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics
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