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 2015 Vol.31 Issue.4,Published 2015-08-31 article
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 337 The Speed of Convergence of the Threshold Version of Bipower Variation for Semimartingales Xiao Xiaoyong, Yin Hongwei In this paper, we consider the speed of convergence of the threshold version of bipower variation for a semimartingale, which is driven by a standard Brownian motion and a pure jump Levy process with possibly infinite activity of the small jumps. 2015 Vol. 31 (4): 337-346 [Abstract] ( 525 ) [HTML 1KB] [ PDF 414KB] ( 1009 )
 347 General Shrinkage Rule with Respect to gamma-Norms for Bridge Estimation Gai Yujie, Zhang Zhanli, Zhang Jun Bridge regression, a special family of penalized regressions of a penalty function $\fn_jvn \100dpi \inline \tsm|\beta_j|^\gamma$ with $\fn_jvn \100dpi \inline \gamma>0$, has been studied in many literatures. In this paper, we provide some theoretical results of how the shrinkage rule changing with $\fn_jvn \100dpi \inline \gamma$ under two settings: $\fn_jvn \100dpi \inline \gamma\geq 1$ and $\fn_jvn \100dpi \inline 0<\gamma<1$, respectively. Simulation results are conducted to evaluate the performance of the proposed method. 2015 Vol. 31 (4): 347-356 [Abstract] ( 666 ) [HTML 1KB] [ PDF 431KB] ( 753 )
 357 Pricing Derivatives under a Markov Skeleton Process Jia Zhaoli, Zhang Fan, Zhang Shuguang In this paper, it is assumed that the underlying is a Markov skeleton process (abbreviated MSP): this process can be better reflecting the instability of the financial market. Using the properties of Markov skeleton process, the characteristic function of the price process is given, combined with fast Fourier transform (FFT) method, the pricing formula of derivatives under the Markov skeleton process is given. The results of this paper can be applied to price other financial derivatives, and it enriching the pricing theory of financial derivatives. 2015 Vol. 31 (4): 357-366 [Abstract] ( 397 ) [HTML 1KB] [ PDF 488KB] ( 841 )
 367 The Periods of States for Markov Chains in a Random Environment Fei Shilong, Bai Yaoqian The periods of states for Markov chains in a random environment are introduced and some properties about periods are investigated. An open problem (Orey, 1991; Problem 1.3.3) is studied under the assumption that states have periods. 2015 Vol. 31 (4): 367-374 [Abstract] ( 584 ) [HTML 1KB] [ PDF 371KB] ( 840 )
 375 The Perturbed Compound Poisson Risk Model with Constant Interest Zhang Yuanyuan, Wang Wensheng This study has considered the compound Poisson risk model perturbed by diffusion with constant interest and obtained an integral-differential equation for the Gerber-Shiu discounted penalty function. Asymptotic expression for the ultimate ruin probability also derived across the study. 2015 Vol. 31 (4): 375-383 [Abstract] ( 446 ) [HTML 1KB] [ PDF 381KB] ( 829 )
 384 Renewal-Geometry Process and Its Properties In this paper, the concept of renewal-geometry process is put forward based on the idea of stage deterioration of system. The definitions of renewal-geometry function, the quasi renewal-geometry age and quasi residual renewal-geometry life for the new stochastic process are given. The related properties of renewal-geometry process are studied. Finally, the related theory results are simulated by an example. 2015 Vol. 31 (4): 384-394 [Abstract] ( 448 ) [HTML 1KB] [ PDF 506KB] ( 630 )
 395 Pricing Catastrophe Options with Stochastic Interest Rates and Compound Poisson Losses Jin Yunguo, Zhong Shouming In this paper, we present an approach of changing probability measures associated with numeraire changes to the pricing of catastrophe event (CAT) derivatives. We assume that the underlying asset and a discounted zero-coupon bond follow a stochastic process, respectively. We obtain explicit closed form formulae that permit the interest rate to be random. We shall see that sometimes it is convenient to change the numeraire because of modeling considerations as well. Furthermore, we show that, for compound Poisson losses, sometimes a continuum of jump sizes can be replaced by finitely many jump sizes. Therefore, sometimes we can explore further applications of the closed-form formulae beyond the case that the compound Poisson losses are finitely many jump sizes. Finally, numerical experiments demonstrate how financial risks and catastrophic risks affect the price of double trigger put option. 2015 Vol. 31 (4): 395-410 [Abstract] ( 488 ) [HTML 1KB] [ PDF 514KB] ( 1035 )
 411 Reward Processes and Performance Optimization in Asymmetric Supermarket Models Li Quanlin, Ding Yuanyuan, Yang Feifei The supermarket model has been an important mathematical tool in the study of resource management in large-scale networks by means of some advantages, such as, simple operations, quick reaction, real-time management and control and so on. It is widely applied in internet of things, cloud computing, cloud manufacturing, big data, transportation, health care and other important practical fields. Up to now, analysis of the asymmetric supermarket models is an increasingly interesting topic in this area.   In this paper, we analyze an asymmetric supermarket model. Because the M servers are different from each other, the routine selection policies of each customer become to have a complex structure, where not only are the routine selection policies related to the different queue lengths and the different service speeds among the M servers, but they are also related to the customer's preference for the M servers. For this, we set up several useful routine selection policies in terms of the decision-making methods. Based on this, we provide the Markov reward processes of the asymmetric supermarket model and establish the associated functional reward equations, give a useful value iterative algorithm for solving the functional reward equations, obtain a criterion of performance evaluation in the asymmetric supermarket model through a double-direction optimization, and show that the sequence of iterative reward functions is monotone and the value iterative algorithm is convergent. This paper provides new and useful highlight on understanding how the asymmetric supermarket model is applied to resource management and control in large-scale networks both from the objective conditions and from the subjective behavior. At the same time, the methodology and main results of this paper give some basic theory and techniques in the study of asymmetric supermarket models for the first time. 2015 Vol. 31 (4): 411-431 [Abstract] ( 414 ) [HTML 1KB] [ PDF 635KB] ( 677 )
 432 Covariate-Adjusted Nonparametric Regression for Time Series Ma Yunyan, Kou Guangjie The covariate-adjusted regression model was initially proposed for the situations where both the predictors and the response variables are not directly observed, but are distorted by some common observable covariates. In this paper, we investigate a covariate-adjusted nonparametric regression (CANR) model and consider the proposed model on time series setting. We develop a two-step estimation procedure to estimate the regression function. The asymptotic property of the proposed estimation is investigated under the $\fn_jvn \100dpi \inline \alpha$-mixing conditions. Both the real data and simulated examples are provided for illustration. 2015 Vol. 31 (4): 432-448 [Abstract] ( 516 ) [HTML 1KB] [ PDF 689KB] ( 782 )

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