参考文献/References:
［1］ 马超群, 马宗刚. 基于 Vasicek 和 CIR 模型的巨灾风险债券定价［J］. 系统工程, 2013, 31(9): 33-38.
MA Chaoqun, MA Zonggang. Pricing catastrophe risk bonds using the Vasicek and CIR models［J］. Systems Engineering, 2013, 31(9): 33-38.(in Chinese)
［2］ 谢卓伦, 陈佳琰, 叶露. 中国大陆地区地震巨灾风险的分布拟合及债券定价［J］. 浙江理工大学学报, 2019, 42(1): 10-19.
XIE Zhuolun, CHEN Jiayan, YE Lu. Distribution fitting of earthquake catastrophe risk and bond pricing in mainland China［J］. Journal of Zhejiang Sci-Tech University, 2019, 42(1): 10-19.(in Chinese)
［3］ 马宗刚, 马超群, 肖时松. 台风风暴潮债券定价——基于我国沿海1989-2015灾害数据［J］. 系统工程, 2017, 35(9): 18-26.
MA Zonggang, MA Chaoqun, XIAO Shisong. Pricing typhoon bonds based on storm surge disaster in coastal areas of China：based on the data from 1989 to 2015［J］. Systems Engineering, 2017, 35(9): 18-26.(in Chinese)
［4］ GEMAN H, YOR M. Stochastic time changes in catastrophe option pricing［J］. Insurance: Mathematics and Economics, 1997, 21(3): 185-193.
［5］ HEYDE C C, WANG D. Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims［J］. Advances in Applied Probability, 2009, 41(1): 206-224.
［6］ 苏必豪, 李婧超. 经典风险模型中破产变量的联合分布［J］.深圳大学学报理工版, 2019, 36(4): 419-423.
SU Bihao, LI Jingchao. The joint distribution of ruin related quantities in the classical risk model［J］.Journal of Shenzhen University Science and Engineering, 2019, 36(4): 419-423.(in Chinese)
［7］ BENSON D A, SCHUMER R, MEERSCHAERT M M. Recurrence of extreme events with power‐law interarrival times［J］. Geophysical Research Letters, 2007, 34(16): L16404.
［8］ MUSSON R M W, TSAPANOS T, NAKAS C T. A power-law function for earthquake interarrival time and magnitude［J］. Bulletin of the Seismological Society of America, 2002, 92(5): 1783-1794.
［9］ SALIM A, PAWITAN Y. Extensions of the Bartlett-Lewis model for rainfall processes［J］. Statistical Modelling, 2003, 3(2): 79-98.
［10］ STOYNOV P, ZLATEVA P, VELEV D, et al. Modelling of major flood arrivals on Chinese rivers by switch-time processes［C］// The 3rd International Conference on Advances in Environment Research. Beijing: IOP Publishing, 2017: 012006.
［11］ REPIN O N, SAICHEV A I. Fractional Poisson law［J］. Radiophysics and Quantum Electronics, 2000, 43(9): 738-741.
［12］ BIARD R, SAUSSEREAU B. Fractional Poisson process: long-range dependence and applications in ruin theory［J］. Journal of Applied Probability, 2014, 51(3): 727-740.
［13］ SCALAS E. A class of CTRWs: compound fractional Poisson processes［M］// KLAFTER J, LIM S C, METZLER R. Fractional dynamics. Hackensack, USA: World Scientific Publication, 2012: 353-374.
［14］ MAHESHWARI A, VELLAISAMY P. On the long-range dependence of fractional Poisson and negative binomial processes［J］. Journal of Applied Probability, 2016, 53(4): 989-1000.
［15］ WANG Ying, WANG Dehui, ZHU Fukang. Estimation of parameters in the fractional compound Poisson process［J］. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(10): 3425-3430.
［16］ SCALAS E, VILES N. On the convergence of quadratic variation for compound fractional Poisson processes［J］. Fractional Calculus and Applied Analysis, 2012, 15(2): 314-331.
［17］ ZHANG Jiesong. Optimal layer reinsurance for compound fractional Poisson model［J］. Discrete Dynamics in Nature and Society, 2019(16): 1-8.
［18］ LASKIN N. Fractional Poisson process［J］. Communications in Nonlinear Science and Numerical Simulation, 2003, 8(3): 201-213.
［19］ JARROW R A. The term structure of interest rates［J］. The Annual Review of Financial Economics, 2009, 1(1): 69-96.
［20］ 谢赤, 吴雄伟. 基于 Vasicek 和 CIR 模型中的中国货币市场利率行为实证分析［J］. 中国管理科学, 2002, 10(3): 22-25.
XIE Chi, WU Xiongwei. An empirical analysis of the interest rate behavior in China’s monetary market using the Vasicek and CIR models［J］. Chinese Journal of Management Science, 2002, 10(3): 22-25.(in Chinese)
［21］ COX S H, PEDERSEN H W. Catastrophe risk bonds［J］. North American Actuarial Journal, 2000, 4(4): 56-82.
［22］ LEE J P, YU M T. Pricing default-risky CAT bonds with moral hazard and basis risk［J］. Journal of Risk and Insurance, 2002, 69(1): 25-44.
［23］ BAI Lihua, CAI Jun, ZHOU Ming. Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting［J］. Insurance: Mathematics and Economics, 2013, 53(3): 664-670.
［24］ JOHNSON M A, TAAFFE M R. Matching moments to phase distributions: mixtures of Erlang distributions of common order［J］. Stochastic Models, 1989, 5(4): 711-743.
［25］ LINDSKOG F, MCNEIL A J. Common Poisson shock models: applications to insurance and credit risk modeling［J］. ASTIN Bulletin: The Journal of the IAA, 2003, 33(2): 209-238.
［26］ BARGES M, COSSETTE H, LOISEL S, et al. On the moments of aggregate discounted claims with dependence introduced by a FGM copula［J］. ASTIN Bulletin: The Journal of the IAA, 2011, 41(1): 215-238.
［27］ BEGHIN L, ORSINGHER E. Fractional Poisson processes and related planar random motions［J］. Electronic Journal of Probability, 2009, 14: 1790-1826.
［28］ 王颖. 复合分数阶泊松过程的参数估计及应用［D］. 长春: 吉林大学, 2015.
WANG Ying. Parameter estimation and application of the fractional compound Poisson process［D］. Changchun: Jilin University, 2015.(in Chinese)