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Insurance claims modulated by a hidden Brownian marked point process

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  • Elliott, Robert J.
  • Chen, Zhiping
  • Duan, Qihong

Abstract

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.

Suggested Citation

  • Elliott, Robert J. & Chen, Zhiping & Duan, Qihong, 2009. "Insurance claims modulated by a hidden Brownian marked point process," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 163-172, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:163-172
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    References listed on IDEAS

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    1. Chian, Abraham C.-L. & Borotto, Felix A. & Rempel, Erico L. & Rogers, Colin, 2005. "Attractor merging crisis in chaotic business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 869-875.
    2. Reinhard, Jean-Marie, 1984. "On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 23-43, April.
    3. Kim, Bara & Kim, Hwa-Sung, 2007. "Moments of claims in a Markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 485-497, May.
    4. Konrad Banachewicz & André Lucas & Aad van der Vaart, 2008. "Modelling Portfolio Defaults Using Hidden Markov Models with Covariates," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 155-171, March.
    5. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    6. Schenk-Hoppe, Klaus Reiner, 2005. "Poverty traps and business cycles in a stochastic overlapping generations economy with S-shaped law of motion," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 275-288, June.
    7. Turner, Rolf, 2008. "Direct maximization of the likelihood of a hidden Markov model," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4147-4160, May.
    8. Ruge-Murcia, Francisco J., 2007. "Methods to estimate dynamic stochastic general equilibrium models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2599-2636, August.
    9. Mohamed Saidane & Christian Lavergne, 2007. "Conditionally heteroscedastic factorial HMMs for time series in finance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(6), pages 503-529, November.
    10. Duffy, John & Xiao, Wei, 2007. "Instability of sunspot equilibria in real business cycle models under adaptive learning," Journal of Monetary Economics, Elsevier, vol. 54(3), pages 879-903, April.
    11. Zhu, Jinxia & Yang, Hailiang, 2008. "Ruin theory for a Markov regime-switching model under a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 311-318, February.
    12. Walde, Klaus, 2002. "The economic determinants of technology shocks in a real business cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 1-28, November.
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    Cited by:

    1. Qihong Duan & Junrong Liu, 2015. "A first step to implement Gillespie’s algorithm with rejection sampling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 85-95, March.
    2. Duan, Qihong & Wei, Ying & Chen, Zhiping, 2014. "Relationship between the benchmark interest rate and a macroeconomic indicator," Economic Modelling, Elsevier, vol. 38(C), pages 220-226.

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