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Chinese Annals of Mathematics,Series B 2018年第5期39卷 773-790页

作者： Siyu LV Zhen WU School of Mathematics Southeast UniversityNanjing 211189China School of Mathematics Shandong UniversityJinan 250100China

The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.

关键词： Stochastic maximum principle Dynamic programming principle Forward-backward stochastic differential equation Regime switching jump diffusion

Necessary Maximum Principle of Stochastic Optimal Control with Delay and jump diffusion

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Communications in Mathematical Research 2014年第3期30卷 245-256页

作者： XING LEI ZHAO PENG-FEI Li Yong College of Basic Sciences Changchun University of Technology Institute of Mathematics Jilin University College of Geoexploration Science and Technology Jilin University Post-doctoral Flow Station of Computer Science and Technology College of Computer Science and TechnologyJilin University Department of Scientific Computing Florida State University

In this paper, we have studied the necessary maximum principle of stochastic optimal control problem with delay and jump diffusion.

关键词： stochastic differential equation jump diffusion delay necessary maximum principle

jump diffusion Modeling of Stock Prices on Ghana Stock Exchange

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1736-1754页

作者： Osei Antwi Kyere Bright Kwasi Awuah Wereko Mathematics & Statistics Department Accra Technical University Accra Ghana Accountancy Department Accra Technical University Accra Ghana Business School Ghana Institute of Public Administration (GIMPA) Accra Ghana

The behaviour of stocks on the Ghana stock exchange is examined to show that stock prices on the exchange are subject to sudden price changes. It is shown that such unexpected events and uncertainties affecting trading on the exchange cannot be modeled solely by the conventional geometric Brownian motion outlined in the Black-Scholes model. A new concise and simpler approach is developed to derive the jump diffusion model and consequently, its suitability to model stocks on the exchange is emphasized and given rigorous treatment. The model is subsequently used to predict the behaviour of stocks using historical stock prices as input parameters. The simulated stock returns are compared to actual returns to determine the model’s suitability to predict the market. The results show that the jump diffusion model is appropriate in predicting the behaviour of approximately 25% percent of stocks listed on the exchange.

关键词： diffusion jump diffusion Skewness Kurtosis jump Sizes

Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments

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Science China Mathematics 2020年第12期63卷 2573-2594页

作者： Ying Xie Chengjian Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China School of Mathematics and Economics Hubei University of EducationWuhan 430205China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with numerical solutions of nonlinear stiff stochastic differential equations with jump-diffusion and piecewise continuous *** combining compensated split-step methods and balanced methods,a class of compensated split-step balanced(CSSB)methods are suggested for solving the *** on the one-sided Lipschitz condition and local Lipschitz condition,a strong convergence criterion of CSSB methods is *** is proved under some suitable conditions that the numerical solutions produced by CSSB methods can preserve the mean-square exponential stability of the corresponding analytical *** numerical examples are presented to illustrate the obtained theoretical results and the effectiveness of CSSB ***,in order to show the computational advantage of CSSB methods,we also give a numerical comparison with the adapted split-step backward Euler methods with or without compensation and tamed explicit methods.

关键词： stiff stochastic differential equation jump diffusion piecewise continuous argument compensated split-step balanced method strong convergence mean-square exponential stability

Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

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Frontiers of Mathematics in China 2014年第4期9卷 965-982页

作者： Jie XIONG Shuaiqi ZHANG Hui ZHAO Xihuan ZENG Department of Mathematics FST University of Macao Macao China School of Economics and Commerce Guangclong University of TechnologyGuangzhou 510520 China Department of Statistics Hebei University of Technology Tianjin 300401 China Department of Mathematics Tianjin University Tianjin 300072 China Institute of Business Administration University of Macao Macao China

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems： the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.

关键词： Inside information investment reinsurance jump diffusion

On Optimal Mean-Field Control Problem of Mean-Field Forward-Backward Stochastic System with jumps Under Partial Information

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Journal of Systems Science & Complexity 2017年第4期30卷 828-856页

作者： ZHOU Qing REN Yong WU Weixing School of Science Beijing University of Posts and Telecommunications Department of Mathematics Anhui Normal University Research Center of Applied Finance and School of Finance and Banking University of International Business and Economics

This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.

关键词： Forward-backward stochastic differential equation Girsanov's theorem jump diffusion Malliavin calculus maximum principle mean-field type partial information.

Asymptotic Expansions of Transition Densities for Hybrid jump-diffusions

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Acta Mathematicae Applicatae Sinica 2004年第1期20卷 1-18页

作者： Yuan-jinLiu G.Yin DepartmentofMathematics WayneStateUniversity.DetroitMI18202

A class of hybrid jump diffusions modulated by a Markov chain is considered in this work. The motivation stems from insurance risk models, and emerging applications in production planning and wireless communications. The models are hybrid in that they involve both continuous dynamics and discrete events. Under suitable conditions, asymptotic expansions of the transition densities for the underlying processes are developed. The formal expansions are validated and the error bounds obtained.

关键词： Markov chain jump diffusion hybrid model Poisson process asymptotic expansion

Path-dependent backward stochastic Volterra integral equations with jumps,differentiability and duality principle

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Probability, Uncertainty and Quantitative Risk 2018年第1期3卷 109-145页

作者： Ludger Overbeck Jasmin A.L.Roder Institute of Mathematics University of GießenArndtsraße 235392 GießenGermany

We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag ***,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with *** a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.

关键词： Path-dependent backward stochastic Volterra integral equation jump diffusion Path-differentiability Duality principle Comparison theorem Functional Ito formula Dynamic coherent risk measure

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

具有跳扩散的美式期权二叉树计算格式的收敛速率

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高等学校计算数学学报 2008年第1期30卷 76-96页

作者：梁进同济大学数学系上海 200092

American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral *** the stability condition （σ;Δt）/（Δx;）≤1,whereΔx=ln（S;+1）/（S;）,the convergence rate O(（Δx）;+（Δt）;)of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.

关键词： American options jump diffusion convergence rate error estimate explicit difference scheme binomial tree method integro-differential equation