Geodesic
Estimation of derivatives with respect to parameters of a~functional of a~diffusion process moving in a domain with absorbing boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 4, pp. 385-404.

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In this paper, a statistical method for estimation of derivatives with respect to parameters of a functional of a diffusion process moving in a domain with absorbing boundary is proposed. The considered functional defines the probability representation of the solution of the corresponding parabolic first boundary value problem. The problem posed is solved by the numerical solution of stochastic differential equations (SDE) by the Euler method. The evaluation of an error of the proposed method is derived, and estimations of variance of the obtained parametric derivatives are given. Some numerical results are presented. 
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S. A. Gusev. Estimation of derivatives with respect to parameters of a~functional of a~diffusion process moving in a domain with absorbing boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 4, pp. 385-404. http://geodesic.mathdoc.fr/item/SJVM_2008_11_4_a3/

[1] Gobet E., Munos R., “Sensitivity analysis using Ito-Malliavin calculus and martingales. Application to stochastic optimal control”, SIAM J. Control Optim., 43:5 (2005), 1676–1713 | DOI | MR | Zbl

[2] Gobet E., Munos R., Sensitivity analysis using Ito-Malliavin calculus and martingales., http://www.cmap.polytechnique.fr/preprint/repository/520.pdf

[3] Gobet E., Costantini C., and Karoui N. El., “Boundary sensitivities for diffusion processes in time dependent domains”, Appl. Math. Optimization, 54:2 (2006), 159–187 | DOI | MR | Zbl

[4] Fournie E. et al., “Applications of Malliavin calculus to Monte Carlo methods in finance”, Finance Stochast., 3:4 (1999), 391–412 | DOI | MR | Zbl

[5] Montero M., Kohatsu-Higa A., “Malliavin calculus applied to Finance”, Physica A, 320 (2003), 548–570 | DOI | MR | Zbl

[6] Gusev S. A., “Otsenki metodom Monte-Karlo proizvodnykh po parametram resheniya parabolicheskogo uravneniya na osnove chislennogo resheniya SDU”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 8:4 (2005), 297–306 | Zbl

[7] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[8] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968 | MR | Zbl

[9] Gobet E., Menozzi S., Stopped diffusion process: overshoots and boundary correction, http://hal.archives-ouvertes.fr/hal-00157975/fr/

[10] Dokuchaev N., “Estimates for distances between first exit times via parabolic equations in unbounded cylinders”, Probab. Theory Relat. Fields, 129 (2004), 290–314 | DOI | MR | Zbl