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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

In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues 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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Keywords 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. Quantitative Finance and Economics, 2018, 2(1): 246-260. doi: 10.3934/QFE.2018.1.246

References

  • 1.Beekman J, Fueling C (1990) Interest and mortality randomness in some annuities. Insur Math Econ 9: 185–196.    
  • 2.Beekman J, Fueling C (1991) Extra randomness in certain annuity models. Insur Math Econ 10: 275–287.
  • 3.Bellhouse DR, Panjer HH (1980)Stochastic modelling of interest rates with applications to life contingencies: Part I. J Risk Insur 47: 91–110.
  • 4.Bellhouse DR, Panjer HH (1981) Stochastic modelling of interest rates with applications to life contingencies: Part II. J Risk Insur 48: 628–637.    
  • 5.Boulier J, Huang S, Taillard G (2001) Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund. Insur Math Econ 28: 173–189.    
  • 6.Bowers NL, Gerber HU, Hickman JC, et al. (1997) Actuarial mathematics, 2 Eds., Schaumburg, IL: Society of Actuaries.
  • 7.Brigo D, Mercurio F (2006) Interest rate models-theory and practice, 2 Eds., Berlin: Springer.
  • 8.Cai J, Dickson DCM (2004) Ruin probabilities with a Markov chain interest model. Insur Math Econ 35: 513–525.    
  • 9.Deng G (2015) Pricing American put option on zero-coupon bond in a jump-extended CIR model. Commun Nonlinear Sci Numer Simulat 22: 186–196.    
  • 10.Dhaene J (1989)Stochastic interest rates and autoregressive integrated moving average processes. Astin Bull 19: 131–138.
  • 11.Dufresne D (2007) Stochastic life annuities. N Am Actuar J 11: 136–157.
  • 12.Hoedemakrs T, Darkiewicz GJ, Goovaerts M (2004) Approximations for life annuity contracts in a stochastic financial environment. Insur Math Econ 37: 239–269.
  • 13.Hu S, Chen S (2016) On the stationary property of a reflected Cox-Ingersoll-Ross interest rate model driven by a Levy process. Chin J Appl Probab Stat 32: 290–300.
  • 14.Klebaner F (2005) Introduction to stochastic calculus with applications, London: Imperial College Press.
  • 15.Li L, Mendoza-Arriaga R, Mitchell D (2016) Analytical representations for the basic affine jump diffusion. Oper Res Lett 44: 121–128.    
  • 16.Li C, Lin L, Lu Y, et al. (2017) Analysis of survivorship life insurance portfolios with stochastic rates of return. Insur Math Econ 75: 16–31.    
  • 17.Li S, Yin C, Zhao X, et al. (2017) Stochastic interest model based on compound Poisson process and applications in actuarial science. Math Probl Eng 1–12.
  • 18.Liang J, Yin H, Chen X, et al. (2017) On a Corporate Bond Pricing Model with Credit Rating Migration Risks and Stochastic Interest Rate. Quanti Financ Econ 1: 300–319.    
  • 19.Parker G (1994a) Moments of the present value of a portfolio of policies. Scand Actuar J 77: 53–67.
  • 20.Parker G (1994b) Stochastic analysis of portfolio of endowment insurance policies. Scand Actuar J 77: 119–130.
  • 21.Parker G (1994c) Two stochastic approaches for discounting actuarial functions. Astin Bull 24: 167–181.
  • 22.Ross SM (1996) Stochastic processes, 2 Eds., New York: John Wiley & Sons, Inc.
  • 23.Zhao X, Zhang B, Mao Z (2007) Optimal dividend payment strategy under stochastic interest force. Qual Quant 41: 927–936.    
  • 24.Zhao X, Zhang B (2012) Pricing perpetual options with stochastic discount interest. Qual Quant 46: 341–349.    

 

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