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Computing survival probabilities based on stochastic differential models. (English) Zbl 1310.65008

Summary: We develop a new numerical method to compute survival probabilities based on stochastic differential models, a matter of great importance in several areas of science, such as finance, biology, medicine and geophysics. This novel approach is based on polynomial differential quadrature, which is combined with a high-order time discretization scheme. Numerical experiments are presented showing that the proposed method performs extremely well and is more efficient than the approaches recently developed in [M. Costabile et al., “Computing finite-time survival probabilities using multinomial approximations of risk models”, Scand. Actuar. J., in press, published online (2013; doi:10.1080/03461238.2013.838603)] and [A. Guarin et al., Eur. J. Oper. Res. 214, No. 3, 805–813 (2011; Zbl 1219.91139)].

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B30 Risk theory, insurance (MSC2010)
92D25 Population dynamics (general)

Citations:

Zbl 1219.91139
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References:

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