RT Report
T1 Applications to risk theory of a Montecarlo multiple integration method
A1 Usábel Rodrigo, Miguel Arturo
AB The evaluation of multiple integrals is a commonly encountered problem in risk theory, specially in ruin probability. Using Monte Carlo simulation we will obtain an unbiased and consistent point estimator, and also confidence intervals as approximations of a special case of multiple integral frequently used in risle theory. The variance reduction achieved compared to straight simulation and some specific properties malee this approach interesting when approximating ruin probabilities.
PB Facultad de Ciencias Económicas y Empresariales. Decanato
SN 2255-5471
YR 1997
FD 1997
LK https://hdl.handle.net/20.500.14352/64129
UL https://hdl.handle.net/20.500.14352/64129
LA eng
NO Bahvalov, N.S. (1959). On approximate calculation of multiple integrals, Vestnik Moscov. Univ. Ser. Mat. Meh. ABt. Fiz. Rim., 4, 3-8.Bratley, P.; Fox, B.L. & Schrage, L.E. (1987). A guide to simulation, Springer-Verlag, New York.Büh1mann,H. (1970). Mathematical methods in Risk Theory. Springer-Verlag, New York.Burden, R.L. and Fau·es, J.D.(1985). Numerical Analysis, P.W.S., Boston.De Vylder, Fo and Goovaerts, M.J. (1988). Recursive Calculation of Finite-time ruin probabilities, Insmance: Mathematics and Economics, 7, 1-7.Fishman, G.S. (1996). Monte Cado: concepts, algorithms and applications. Springer series in operations research. Springer-Verlag, New York.Haber, S. (1970). Numerical evaluation of multiple integrals, SIAM Rev., 12, 481-526.Niederreiter, H. (1978). Quasi-Monte Cario methods and pseudorandom numbers, Bull. Amer. l'vfath. Soco, 84, 957-1041. - (1992). Random number generation and Quasi-Monte Cario methods, Society for industrial and applied mathematics, Philadelphia, PA.Panjer, H.H. (1981). Recursive evaluation of a family of compound distributions, ASTlN Bulletin, 12, 22-26.Panjer, H.H. & Willrnot, G.E. (1992). Ins'urance risk Models, Society of Actuaries, Schaumbmg.Rubulsteul, R.y. (1981). Simulation and the Monte Cado Meihod, Wiley, New York.Usábel, M.A. (1995). Cálculo numérico de probabilidades de ruina: Aplicación de la teoría de la renovación y de la simulación, Unpublished Ph. D. Thesis, Department of Finance and actuarial science, Universidad Complutense de Madrid, Spain. - (1995). A numerical method of estimating ruin probabilities in a simple financial model, Proc. XXV International Congress of Actuaries, September 1995, Brussels.
DS Docta Complutense
RD 8 may 2024