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Thiele’s differential equation with stochastic interest of diffusion type. (English) Zbl 0845.62077

Summary: The classical Thiele’s differential equation for the prospective reserve of an insurance policy has been generalized to models with counting process driven payments and deterministic interest. Here the result is extended to situations with diffusion driven stochastic interest. The technique of proof consists in identifying the null part of the martingale associated with the initial present value of the payments. The presentation centers on life insurance, but the theory can be adapted to more general stochastic payment streams.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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