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

Shilong Li; Xia Zhao; Chuancun Yin; Zhiyue Huang; Shilong Li; Xia Zhao; Chuancun Yin; Zhiyue Huang

doi:10.3934/QFE.2018.1.246

Quantitative Finance and Economics

2018, Volume 2, Issue 1: 246-260. doi: 10.3934/QFE.2018.1.246

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Research article

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

1.
School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China
2.
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
3.
MRC Biostatistics Unit, University of Cambridge, Cambridge, CB2 0SR, UK

Received: 16 January 2018 Accepted: 29 January 2018 Published: 13 March 2018
JEL Codes: G22

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. Our numerical results show actuarial values could be sensitive to the parameters and distribution settings, which shows the importance of introducing this kind interest model.
- compound Poisson process,
- Brownian motion,
- force of interest,
- expected discounted function,
- life annuity,
- actuarial present values
Citation: Shilong Li, Xia Zhao, Chuancun Yin, Zhiyue Huang. Stochastic interest model driven by compound Poisson process and Brownian motion with applications in life contingencies[J]. Quantitative Finance and Economics, 2018, 2(1): 246-260. doi: 10.3934/QFE.2018.1.246

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Abstract

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. Our numerical 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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