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Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

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  • Shilong Li
  • Chuancun Yin
  • Xia Zhao
  • Hongshuai Dai

Abstract

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Suggested Citation

  • Shilong Li & Chuancun Yin & Xia Zhao & Hongshuai Dai, 2017. "Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, May.
    • Handle: RePEc:hin:jnlmpe:3472319
    DOI: 10.1155/2017/3472319
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    Cited by:

    1. Freud, Thomas & Rodriguez, Pablo M., 2023. "The Bell–Touchard counting process," Applied Mathematics and Computation, Elsevier, vol. 444(C).

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