Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

Large Deviation Principle for a Form of Compound Nonhomogeneous Poisson Process

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.

Poisson Process Modeling of Pure Jump Equities on the Ghana Stock Exchange

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.

Insurance ratemaking method for risk of construction diversion project

Based on analyzing risk factors of diversion project,synthetic risk rate and engineering insurance period,the frequency and distribution law of loss are researched on the grounds that foundation pit is submerged after diversion project ceases to be effective.And then,the standpoint that these total loss is subject to non-homogeneous compound Poisson processes is put forward.Furthermore,the collective risk model of the total loss about engineering insurance is established on the basis of construction diversion project risk.Ultimately,insurance ratemaking method for construction engineering risk and its mathematical expression are presented,which provides theoretical method for the insurance ratemaking of hydropower engineering to some extent.

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

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 jumps.Subsequently, 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.

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

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.

Optimal Dividend Strategies in a Double Compound Poisson Risk Process

In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certain boundary conditions for the present value of dividends until ruin. When the claims from both classes are exponentially distributed, we show that the threshold dividend strategy is an optimal dividend strategy.

Evaluation of call options

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.

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

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.

Some Results behind Dividend Problems

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.

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

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.

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

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.

An M^([X])/G/1 Retrial G-queue with Single Vacation Subject to the Server Breakdown and Repair

An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.