Optimal importance sampling for continuous Gaussian fields

• Autorzy: Pacchiarotti Barbara

Identyfikatory

DOI

10.1515/jaa-2020-2022

• Języki publikacji: EN

Abstrakty

EN

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), no. 2, 255-271], [D. Dufresne, The integral of geometric Brownian motion, Adv. in Appl. Probab. 33 (2001), no. 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), no. 3, 511-524] and [V. R. Fatalov, On the Laplace method for Gaussian measures in a Banach space, Theory Probab. Appl. 58 (2014), no. 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.

Słowa kluczowe

EN

importance sampling; Gaussian field; large deviations

PL

próbkowanie ważone; pole gaussowskie; odchylenie

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2020
• Tom: Vol. 26, nr 2
• Strony: 161--171
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Pacchiarotti Barbara

• Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy

Bibliografia

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• [15] N. Privault and W. I. Uy, Monte Carlo computation of the Laplace transform of exponential Brownian functionals, Methodol. Comput. Appl. Probab. 15 (2013), no. 3, 511-524.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).