Optimal importance sampling for continuous Gaussian fields
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Barbara Pacchiarotti
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.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
Artikel in diesem Heft
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
