Notes on discrete compound Poisson model with applications to risk theory

作者：Zhang, Huiming; Liu, Yunxiao; Li, Bo^*

来源：Insurance: Mathematics and Economics , 2014, 59: 325-336.

DOI：10.1016/j.insmatheco.2014.09.012

• Compound Poisson distribution
• Integer-valued Levy process
• CreditRisk plus model
• Geometric Brownian motion with jumps
• Pseudo compound Poisson distribution
• Wiener-Levy theorem

Probability generating p.g.f.) is a powerful tool to study discrete compound Poisson (DCP) distribution. By applying inverse Fourier transform of p.g.f., it is convenient to numerically calculate probability density and do parameter estimation. As an application to finance and insurance, we firstly show that in the generalized CreditRisk model, the default loss of each debtor and the total default of all debtors are both approximately equal to a DCP distribution, and we give Le Cam's error bound between the total default and a DCP distribution. Next, we consider geometric Brownian motion with DCP jumps and derive its rth moment. We establish the surplus process of the difference of two DCP distributions, and numerically compute the tail probability. Furthermore, we define the discrete pseudo compound Poisson (DPCP) distribution and give the characterizations and examples of DPCP distribution, including the strictly decreasing discrete distribution and the zero-inflated discrete distribution with P(X = 0) > 0.5.

• 出版日期2014-11
• 单位华中师范大学