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	1. On the Complete Monotonicity of the Compound Geometric Convolutionwith Applications in Risk Theory
	CHIU Sung-Nok,YIN Chuancun
	Mathematics 16 November 2012
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	Abstract:This paper proves that the complete monotonicity is preserved under mixedgeometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.
	TO cite this article:CHIU Sung-Nok,YIN Chuancun. On the Complete Monotonicity of the Compound Geometric Convolutionwith Applications in Risk Theory[OL].[16 November 2012] http://en.paper.edu.cn/en_releasepaper/content/4496097


	2. European option pricing and hedging with both fixed and proportional transaction costs under the fractional Black-Scholes model
	ZHANG Ningling,WANG Xiaotian
	Mathematics 15 November 2012
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	Abstract:This paper deals with the problem of discrete time option pricing using the fractional Black-Scholes model with both fixed and proporational transaction costs.Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained. The pseudo-super-replicating price of an option under both fixed and proporational transaction costs is obtained.
	TO cite this article:ZHANG Ningling,WANG Xiaotian. European option pricing and hedging with both fixed and proportional transaction costs under the fractional Black-Scholes model[OL].[15 November 2012] http://en.paper.edu.cn/en_releasepaper/content/4495215

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	3. Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications
	SHI Jingtao
	Mathematics 26 October 2012
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	Abstract:This paper is concerned with the relationshipbetween maximum principle and dynamic programming forstochastic recursive optimal control problems.Under certain differentiability conditions, relations among the adjointprocesses, the generalized Hamiltonian function and the valuefunction are given. A linear quadratic recursive utility portfoliooptimization problem in the financial market is discussed as an explicitly illustrated example of the main result.
	TO cite this article:SHI Jingtao. Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications[J].


	4. Perturbed risk model with a two-step premium rate
	YU Dong,JI Xiaoning
	Mathematics 28 May 2012
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	Abstract:In this paper, we consider the surplusprocess satisfying a perturbed risk model with a two-step premiumand investigate Laplace transform of the first passage time across agiven level before ruin for such surplus process. The approach is via the strong Markov property and shift operator.The result is usedto derive the joint distribution of the maximal surplus before ruin,the surplus immediately before ruin and the deficit at ruin, associated with the ruin time.
	TO cite this article:YU Dong,JI Xiaoning. Perturbed risk model with a two-step premium rate[OL].[28 May 2012] http://en.paper.edu.cn/en_releasepaper/content/4479978


	5. Moderate deviations for estimators of financial risk under an asymmetric Laplace law
	CAI Yujie,GAO Fuqing,WANG Shaochen
	Mathematics 12 March 2012
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	Abstract:We study moderate deviations of estimators of financial risk under an asymmetric Laplace law. The moderate deviation principles of three kinds of estimators based on parametric and non-parametric methods of VaR and CVaR are obtained by the approximation method and the delta method in large deviations. We also present some numerical comparisons of the estimators.
	TO cite this article:CAI Yujie,GAO Fuqing,WANG Shaochen. Moderate deviations for estimators of financial risk under an asymmetric Laplace law[OL].[12 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4470949


	6. Moderate deviations and central limit theorem for small perturbation Wishart processes
	CHEN Lei,GAO Fuqing,WANG Shaochen
	Mathematics 12 March 2012
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	Abstract:Let Xε be a small perturbation Wishart process,i.e., the process Xε/ε is a Wishart process withdimension ρ/ε, starting at x/ε. In this paper, we prove that (Xε t-X 0 t)/√￣εh2(ε) satisfies a large deviation principle, and (Xεt-X 0 t)/√￣ε converges to a Gaussian process, where h(ε)→+∞ and √￣εh(ε)→0 asε→0 We also obtain a moderate deviation principle and a functional central limit theorem for the eigenvalue process of Xε by delta method and matrix perturbation theory.
	TO cite this article:CHEN Lei,GAO Fuqing,WANG Shaochen. Moderate deviations and central limit theorem for small perturbation Wishart processes[OL].[12 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4470943


	7. Phase Changes in the Topological Indices of Scale-free Trees
	FENG Qunqiang,HU Zhishui
	Mathematics 18 January 2012
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	Abstract:A scale-free tree with the parameter β is very close to a star if βis just a bit larger than -1, whereas it is close to a randomrecursive tree if β is very large. Through the Zagreb index, the whole scene of the evolution of the scale-free trees model is consideredas β goes from -1 to +∞. And the first two moments and the asymptotic behaviors of this index of a scale-free tree are obtained for all β>-1.
	TO cite this article:FENG Qunqiang,HU Zhishui. Phase Changes in the Topological Indices of Scale-free Trees[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4462894


	8. The Hitting Time for a Cox Risk Process
	Wu Rong ,Wang Wei
	Mathematics 18 January 2012
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	Abstract:This paper investigates the hitting timeand the last exit time of a Cox risk process whose intensity processis a markovian jump process. By a ``backward differential argument"and the Markov property of the intensity process, we derive theintegro-differential equation satisfied by the Laplace transform ofthe hitting time. Exact solution to this equation could beconstructed by the probability method. Further, we investigate thesituation when the intensity process is an n-state Markov process
	TO cite this article:Wu Rong ,Wang Wei . The Hitting Time for a Cox Risk Process[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4457932


	9. Upper bounds for ruin probabilities under stochastic interest rateand optimal investment strategies
	Jinzhu Li,Rong Wu
	Mathematics 29 December 2011
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	Abstract:In this paper, we study the upper bounds for ruin probabilities of aninsurance company which invests its wealth in a stock and a bond. We assumethe interest rate of the bond is stochastic and it is described by aCox-Ingersoll-Ross (CIR) model. For the stock price process, we considerboth the case of constant volatility (driven by an O-U process) and the caseof stochastic volatility (driven by a CIR model). In each case, undercertain conditions, we obtain the minimal upper bound for ruin probabilityas well as the corresponding optimal investment strategy by a pureprobabilistic method.
	TO cite this article:Jinzhu Li,Rong Wu. Upper bounds for ruin probabilities under stochastic interest rateand optimal investment strategies[OL].[29 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4457935


	10. Stability of nonlinear stochastic Volterra difference equations with continuous time
	CHEN Ling,GUO Lifang,CHEN Min
	Mathematics 10 May 2011
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	Abstract:In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time. Lyapunov functionals are used to study the hereditary systems about problems of stability and optimal control. Besides, Lyapunov functionals construction has been widely used to discuss the stability for stochastic differential equations with delay and for stochastic difference equations with discrete time. Based on the general method of Lyapunov functionals construction, the stability of nonlinear stochastic Volterra difference equations is studied here. Particularly, the system considered here have continuous time. Sufficient conditions are obtained not only to ensure the mean square stability to nonlinear stochastic Volterra difference equations with continuous time but also the asymptotical mean square quasi-stability for this system. Furthermore, it is easy to know the considered system is mean square integrable when the system here is asymptotical mean square quasi-stable.
	TO cite this article:CHEN Ling,GUO Lifang,CHEN Min. Stability of nonlinear stochastic Volterra difference equations with continuous time[OL].[10 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4425936

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