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Engineering Analysis with Boundary Elements, Volume 36, Issue 11, November 2012, Pages 1546-1554
Luca Vincenzo Ballestra, Graziella Pacelli
Dipartimento di Strategie Aziendali e Metodologie Quantitative, Seconda Università di Napoli, Corso Gran Priorato di Malta, 81043 Capua, Italy
Dipartimento di Management, Università Politecnica delle Marche, Piazza Martelli 8, 60121 Ancona, Italy
Abstract
We consider the problem of computing the survival (first-passage) probability density function of jump-diffusion models with two stochastic factors. In particular the Fokker–Planck partial integro-differential equation associated to these models is solved using a meshless collocation approach based on radialbasis functions (RBF). To enhance the computational efficiency of the method, the calculation of the jump integrals is performed using a suitable Chebyshev interpolation procedure. In addition, the RBF discretization is carried out in conjunction with an ad hoc change of variables, which allows to use radial basis functions with equally spaced centers and at the same time yields an accurate resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented showing that the RBF approach is extremely accurate and fast, and performs significantly better than the conventional finite difference method.
