THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is investigated in terms of the q-pair q(x)-q(x, A).

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

Two-Sided First Exit Problem for Jump Diffusion Distribution Processes Having Jumps with a Mixture of Erlang

In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.

Insiders' Hedging for Jump Diffusion Processes with Applications to Index Tracking

The hedging problem for insiders is very important in the financial market.The locally risk minimizing hedging was adopted to solve this problem.Since the market was incomplete,the minimal martingale measure was chosen as the equivalent martingale measure.By the F-S decomposition,the expression of the locally risk minimizing strategy was presented.Finally,the local risk minimization was applied to index tracking and its relationship with tracking error variance (TEV)-minimizing strategy was obtained.

Poincaré Inequalities for Bounded Jump Processes

A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfying Poincaré inequality by using isoperimetric constants. It is λ0≥k0^2/（2R） and λ1 ≥k1^2/（2R）.

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.

SYMMETRIC INTEGRAL AND CANONICAL EXTENSION FOR JUMP PROCESS SOME COMBINATORIAL RESULTS

Using approximation technique, we introduce the concepts of canonical extension and symmetrio integral for jump process and obtain some results in the chaotic form.

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

Temperature dependence of multi-jump magnetic switching process in epitaxial Fe/MgO(001) films

Temperature dependence of magnetic switching processes with multiple jumps in Fe/MgO（001） films is investigated by magnetoresistance measurements. When the temperature decreases from 300K to 80K, the measured three-jump hysteresis loops turn into two-jump loops. The temperature dependence of the fourfold in-plane magnetic anisotropy constant K1, domain wall pinning energy, and an additional uniaxial magnetic anisotropy constant KUare responsible for this transformation. The strengths of K1 and domain wall pinning energy increase with decreasing temperature, but KU remains unchanged. Moreover, magnetization reversal mechanisms, with either two successive or two separate 90°domain wall propagation, are introduced to explain the multi-jump magnetic switching process in epitaxial Fe/MgO（001） films at different temperatures.

THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

Integro-Differential Equations for a Jump-Diffusion Risk Process with Dependence between Claim Sizes and Claim Intervals

The classical Poisson risk model in ruin theory assumed that the interarrival times between two successive claims are mutually independent, and the claim sizes and claim intervals are also mutually independent. In this paper, we modify the classical Poisson risk model to describe the surplus process of an insurance portfolio. We consider a jump-diffusion risk process compounded by a geometric Brownian motion, and assume that the claim sizes and claim intervals are dependent. Using the properties of conditional expectation, we establish integro-differential equations for the Gerber-Shiu function and the ultimate ruin probability.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

基于跳聚集现象随机波动率短期利率模型的影响研究

构建了具有自我激励机制跳的随机波动率短期利率模型,应用Hawkes过程描述自我激励机制的跳,从而刻画了跳的聚集现象。基于微分算子展开给出精确的矩函数,进一步应用广义矩方法给出模型的参数估计值和统计推断。实证结果揭示了在随机波动模型条件下,引入自我激励机制跳的模型将不会明显地改变了拟合效果,但是在统计意义上接受强度满足Hawkes过程,而且所构建的模型也能很好地刻画跳的聚集现象。最后,使用过滤方法给出随机波动率、跳的幅度、跳的概率和随机跳强度的估计,特别是跳的概率估计值可作为市场压力测试的一个重要指标。

南海洋脊跃迁的深地震探测数据分析

洋脊跃迁事件是海底扩张阶段受强烈构造和岩浆作用的普遍现象,地球物理资料表明洋脊跃迁事件存在于南海多期次海底扩张过程中,然而关于洋脊跃迁的深部速度结构特征尚不清楚.2021年国家自然科学基金共享航次实施了深地震探测测线OBS2021-1,该测线横穿南海东部次海盆洋脊跃迁(J3)区域.本文介绍了该测线数据的采集情况,完成了导航文件(Ukooa文件)的制作、原始数据的格式转换、炮点位置和海底地震仪(OBS)位置校正的前期数据处理工作.结果表明,OBS2021-1测线数据质量良好,经过炮点和OBS位置校正后,OBS综合地震记录剖面可识别出多组清晰的P波震相,包括Pw、Pg、PmP以及Pn震相.根据同船采集的多道地震处理解释和国际大洋发现计划(IODP)钻探数据,建立了沿测线的初始速度模型.使用RayInvr软件初步获得了OBS2021-1测线下方的正演速度结构模型,识别洋脊跃迁的深部速度结构特征.数据处理结果表明南海洋脊跃迁的地壳厚度增厚,在多道地震剖面上存在渐新世地层的缺失,为进一步研究南海洋脊跃迁过程与构建南海形成演化历史奠定了研究基础.

基于混合次分数跳过程的亚式期权模糊定价

考虑到金融资产价格的长记忆性及跳跃现象,基于混合次分数布朗运动和泊松过程,建立了几何亚式期权定价模型;进一步考虑金融市场模糊性,引入模糊理论得到模糊定价模型.首先,得到混合次分数跳过程Ito∧公式及其股价所满足随机微分方程的解析解;其次,运用风险中性原理给出几何亚式期权的定价公式;然后,运用模糊理论构建了几何亚式模糊期权定价模型;最后,数值模拟分析了置信度和Hurst指数对模糊价格的影响,并将本文所建立模型与经典BS模型进行对比.结果表明,在相应的置信度下模糊定价模型能够给出较为合理的价格区间,有助于金融投资者的决策,从而验证了模型的合理性和实用性.

Exponential stability of stochastic generalized porous media equations with jump

Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.

HOMEOMORPHISM FLOWS FOR NON-LIPSCHITZ SDES DRIVEN BY LVY PROCESSES

In this article, homeomorphism flows for non-Lipschitz stochastic differential equations driven by Levy processes are studied.

Markovian risk process

A Markovian risk process is considered in this paper, which is the generalization of the classical risk model. It is proper that a risk process with large claims is modelled as the Markovian risk model. In such a model, the occurrence of claims is described by a point process {N（t）}t≥0 with N（t） being the number of jumps during the interval （0, t] for a Markov jump process. The ruin probability ψ（u） of a company facing such a risk model is mainly studied. An integral equation satisfied by the ruin probability function ψ（u） is obtained and the bounds for the convergence rate of the ruin probability ψ（u） are given by using a generalized renewal technique developed in the paper.