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An explicit compound poisson process-based shock deterioration model for reliability assessment of aging structures

Journal of Traffic and Transportation Engineering(English Edition) 2022年第3期9卷 461-472页

作者： Cao Wang School of Civil Mining and Environmental EngineeringUniversity of WollongongWollongongNW 222Austalia Department of Civil Engineering Monash UniversityClaytonVic 3800Australia

Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments(mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented,which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed(a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary poisson process of random ***, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the timedependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure,and this effect is enhanced by a smaller occurrence rate of the shock deterioration.

关键词： Structural reliability Resistance degradation compound poisson process Shock deterioration W-function

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Some Results for the compound poisson process That Is Perturbed by Diffusion

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Acta Mathematicae Applicatae Sinica 2002年第1期18卷 153-160页

作者： Chun-sheng ZHANG, Lian-zeng ZHANG, Rong WUDepartment of Mathematics, Nankai University, Tianjing 300071, China Department of Mathematics Nankai University Tianjing China

In the present paper surplus process perturbed by diffusion are considered. The distributions of the surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation and ruin caused by a claim are studied. Some joint distribution densities are obtained. Techniques from martingale theory and renewal theory are used.

关键词： compound poisson process Diffusion Ruin Probability Oscillation Claim Surplus Joint distribution

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Large Deviation Principle for a Form of compound Nonhomogeneous poisson process

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Journal of Donghua University(English Edition) 2011年第2期28卷 217-221页

作者：杨文权胡亦钧 School of Mathematics and Computer Science Jianghan University School of Mathematics and Statistics Wuhan University

By the Cramér method, the large deviation principle for a form of compound poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous poisson process with intensity λ(t)>0, Xi, i≥1, are i.i.d. nonnegative random variables independent of N(t), and h(t), t>0, is a nonnegative monotone real function. Consequently, weak convergence for S(t) is also obtained.

关键词： large deviation principle compound poisson process weak convergence

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poisson process Modeling of Pure Jump Equities on the Ghana Stock Exchange

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Journal of Applied Mathematics and Physics 2022年第10期10卷 3101-3120页

作者： Osei Antwi Kyere Bright Martinu Issa Mathematics & Statistics Department Accra Technical University Accra Ghana Accountancy Department Accra Technical University Accra Ghana Research Department Fair Wages & Salaries Commission Accra Ghana

Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.

关键词： poisson process Pure Jump process compound poisson process Jump Diffusion

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A Continuum Percolation Model for Stock Price Fluctuation as a Lévy process

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Journal of Systems Science & Complexity 2015年第1期28卷 175-189页

作者： WANG Ning RONG Ximin DONG Guanghua College of Management and Economics Tianjin University Department of Science and Technology of Information Tianjin University of Finance and Economics School of Science Tianjin University Center for Applied Mathematics of Tianjin University Department of Mathematics Tianjin Polytechnic University

This paper concerns with two reasons for stock price fluctuation, the instinctive stochastic fluctuation and the fluctuation caused by the spread of information. They are constructed by compound poisson process and continuum percolation model separately. Combining the two models, the authors get a Levy process for the price fluctuation that can explain the fat-tail phenomenon in stock market. The fat-tails axe also presented in numerical simulations.

关键词： compound poisson process continuum percolation fat-tail phenomenon Levy process.

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The dividend function in the jump-diffusion dual model withbarrier dividend strategy

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Applied Mathematics and Mechanics(English Edition) 2008年第9期29卷 1239-1249页

作者：李波吴荣 School of Mathematical Sciences and LPMC Nankai University

A dual model of the perturbed classical compound poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.

关键词： compound poisson process diffusion process Gerber-Shiu function integro-differential equation time of ruin surplus before ruin deficit at ruin

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Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

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Science China Mathematics 2012年第11期55卷 2335-2346页

作者： QIAN LinYi WANG RongMing WANG Shuai School of Finance and Statistics East China Normal UniversityShanghai 200241China Research Center of International Finance and Risk Management East China Normal UniversityShanghai 200241China

This paper extends the model and analysis of Lin, Tan and Yang （2009）. We assume that the financial market follows a regime-switching jump-diffusion model and the mortality satisfies Levy process. We price the point to point and annual reset EIAs by Esscher transform method under Merton＇s assumption and obtain the closed form pricing formulas. Under two cases： with mortality risk and without mortality risk, the effects of the model parameters on the EIAs pricing are illustrated through numerical experiments.

关键词： compound poisson process Levy process stochastic mortality regime-switching equity-indexedannuity

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Some Results behind Dividend Problems

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Acta Mathematicae Applicatae Sinica 2006年第4期22卷 681-686页

作者： Ming Zhou Li Wei Jun-yi Guo School of Mathematical Science Nankai University Tianjin 300071 China School of Finance Renmin University of China Beijing 100872 China

We consider the basic dividend problem of the compound poisson model with constant barrier strategy. Some results concealed behind the dividend problem are made explicit in the present work. Different methods and some of which are firstly given in this paper. All these results presented certain direct relationship between some important actuary variables in classical risk theory is also revealed.

关键词： compound poisson process discount dividend payments integro-differential equation change of measure shift operator

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Evaluation of call options

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Journal of Chongqing University 2002年第2期1卷 89-92页

作者：陈道平 Department of Mathematics and Computer Chongqing Normal University

The European and American call options, for which the prices of their underlying asset follow compound poisson process, are evaluated by a probability method. Formulas that can be used to evaluate the options are obtained, which include not only the elements of an option: the price of the call option, the exercise price and the expiration date, but also the riskless interest rate, nevertheless exclude the volatility of the underlying asset. In practice, the evaluated results obtained by these formulas can provide references of making strategic decision for an investor who buys the call option and a company who sells the call option.

关键词： call option exercise price underlying asset compound poisson process potential no loss probability

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