Stochastic interest model driven by compound Poisson process and Brownian motion with applications in life contingencies

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Li, Shilong 
Xia, Zhao 
Chuancun, Yin 
Huang, Z 

In this paper, we introduce a class of stochastic interest model driven by a compound Poisson process and a Brownian motion, in which the jumping times of force of interest obeys compound Poisson process and the continuous tiny fluctuations are described by Brownian motion, and the adjustment in each jump of interest force is assumed to be random. Based on the proposed interest model, we discuss the expected discounted function, the validity of the model and actuarial present values of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.

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Quantitative Finance and Economics
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