﻿ 应用概率统计

 Office Online
 Journal Online

Current Issue

 2015 Vol.31 Issue.5,Published 2015-10-31 article
 article
 449 Extended a Class of Singular Stochastic Control Models of "Fail-Stop" Wu Qingyu, Sun Shiliang, Huang Xiaoqian This paper extends a class of discount problem of singular stochastic control with stopping time. We extend the state process and cost function to general case. By stochastic analysis and optimal control theory, the "fail-stop" control strategy is its optimal control. The conditions of the "fail-stop" strategy and optimal control function and control method are given. The conclusion in this paper has a fairly deep application. 2015 Vol. 31 (5): 449-456 [Abstract] ( 322 ) [HTML 1KB] [ PDF 471KB] ( 688 )
 457 The Credibility Models with Risks Dependence Structure under Balanced Loss Function Li Xinpeng, Wu Lijun In classical credibility theory, the claim amounts of different insurance policies in a portfolio are assumed to be independent and the premiums are derived under squared-error loss function. Wen et al. (2012) studied the credibility models with a dependence structure among the claim amounts of one insurance policy that is called time changeable effects and obtained the credibility formula. In this paper, we generalized this dependence structure called time changeable effects to the claim amounts of different insurance policies in a portfolio. Credibility premiums are obtained for Buhlmann and Buhlmann-Straub credibility models with dependence structure under balanced loss function. 2015 Vol. 31 (5): 457-468 [Abstract] ( 336 ) [HTML 1KB] [ PDF 396KB] ( 791 )
 469 Log-Operator Scaling Random Fields Zhang Hua In this paper, we present a logarithm representation of operator scaling stable random fields which in particular contains a class of Log-fractional stable motion $\fn_jvn \100dpi \inline \{\Delta_{\log}(x),x\geq 0\}$, and investigate the related sample paths regularity. 2015 Vol. 31 (5): 469-482 [Abstract] ( 300 ) [HTML 1KB] [ PDF 404KB] ( 1051 )
 483 Integro-Differential Equations for Option Prices in Markov Switching Exponential Levy Models Song Ruili, Wang Bo We consider a Markov switching exponential Levy model in which the underlying economy switches between a finite number of states. The switching is modeled by a hidden Markov chain. We explore the link between options prices in Markov switching exponential Levy models and the related partial integro-differential equations in the case of European options. 2015 Vol. 31 (5): 483-492 [Abstract] ( 215 ) [HTML 1KB] [ PDF 408KB] ( 697 )
 493 Rate of Algebraic Convergence for Diffusion Processes on Non-Convex Manifold Cheng Lijuan, Wang Yingzhe Algebraic convergence in $\fn_jvn \100dpi \inline L^2$-sense is studied for the reflecting diffusion processes on noncompact manifold with non-convex boundary. A series of sufficient and necessary conditions for the algebraic convergence are presented. 2015 Vol. 31 (5): 493-502 [Abstract] ( 406 ) [HTML 1KB] [ PDF 407KB] ( 569 )
 503 Ruin Probabilities for One Class of Bivariate Risk Model with Correlated Aggregate Claims under Sparse Processes Wu Chuanju, Wang Xiaoguang, He Xiaoxia, Liu Luqin The paper considers a risk model with two dependent classes of insurance business. In this model, the two claim number processes are partly sparsely correlated through an Erlang(2) process. By introducing an auxiliary model, we obtain the integral equations for ultimate ruin probabilities, and discuss the asymptotic property of ruin probabilities by renewal approach. We also get the linear differential equations of ruin probabilities of the model and the corresponding auxiliary model when claims follow the exponential distributions, and show how solves the linear differential equations by a specific example. 2015 Vol. 31 (5): 503-513 [Abstract] ( 274 ) [HTML 1KB] [ PDF 446KB] ( 679 )
 514 Semiparametric Rate Model for Recurrent Event Data with Cure Rate Zeng Xiaofeng, Chen Chuanzhong, Li Ni Recurrent event data usually occur in long-term studies which concern recurrence rates of the disease. In studies of medical sciences, patients who have infected with the disease, like cancer, were conventionally regarded as impossible to be cured. However, with the development of medical sciences, recently those patients were found to be possibly recovered from the disease. The recurrence rate of the events, which is of primary interest, may be affected by the cure rate that may exist. Therefore, we proposed semiparametric statistical analysis for recurrent event data with subjects possibly being cured. In our approach, we present a proportional rate model for recurrence rate with the cure rate adjusted through a Logistic regression model, and develop some estimating equations for estimation of the regression parameters, with their large sample properties, including consistency and asymptotic normality established. Numerical studies under different settings were conducted for assessing the proposed methodology and the results suggest that they work well for practical situations. The approach is applied to a bladder cancer dataset which motivated our study. 2015 Vol. 31 (5): 514-526 [Abstract] ( 243 ) [HTML 1KB] [ PDF 506KB] ( 764 )
 527 A Note on Discrete Approximation for Excursions of Diffusion Process He Ping In this paper we describe the excursions from a set explicitly for recurrent Markov chain with discrete time. A new exit system is presented through using a law conditioned by specifying the starting point and ending point of excursions. In a simple case, we verify that our conditioned excursion law is a discrete approximation for that of a diffusion. 2015 Vol. 31 (5): 527-538 [Abstract] ( 245 ) [HTML 1KB] [ PDF 395KB] ( 444 )
 539 Usual Multivariate Stochastic Order on the Proportional Reversed Hazard Rates Model Fang Longxiang, Yang Fang Let $\fn_jvn \100dpi \inline X_i\sim F^{\alpha_i}$, $\fn_jvn \100dpi \inline Y_i\sim F^{\gamma_i}$, $\fn_jvn \100dpi \inline i=1,2,\ldots,n$, be all independent PRHR variables. Firstly, we show that $\fn_jvn \100dpi \inline (\alpha_1,\alpha_2,\ldots,\alpha_n)\succeq_{\text{m}}(\gamma_1,\gamma_2,\ldots,\gamma_n)$implies $\fn_jvn \100dpi \inline (Y_{1:n},Y_{2:n},\ldots,Y_{n:n})\geq_{\text{st}}(X_{1:n},X_{2:n},\ldots,X_{n:n})$. Secondly, we consider the comparison of convolutions of independent heterogeneous PRHR variables with respect to the usual stochastic ordering. Suppose $\fn_jvn \100dpi \inline \alpha_1\geq\alpha_2\geq\cdots\geq\alpha_n$ and $\fn_jvn \100dpi \inline \gamma_1\geq\gamma_2\geq\cdots\geq\gamma_n$, we prove that $\fn_jvn \100dpi \inline (\alpha_1,\alpha_2,\ldots,\alpha_n)\succeq_{\text{m}}(\gamma_1,\gamma_2,\ldots,\gamma_n)$ implies $\fn_jvn \100dpi \inline \tsm_{r=k}^nY_r\geq_{\text{st}}\tsm_{r=k}^nX_r$, for all $\fn_jvn \100dpi \inline 1\leq k\leq n$. The results established here strengthen some of the results known in the literature. 2015 Vol. 31 (5): 539-546 [Abstract] ( 332 ) [HTML 1KB] [ PDF 390KB] ( 502 )
 547 Smoothness of the Collision Local Times of Sub-Fractional Brownian Motions Shen Guangjun, Li Mengyu Let $\fn_jvn \100dpi \inline S^{H_i}=\{S^{H_i}_t,t\geq 0\}$, $\fn_jvn \100dpi \inline i=1,2$ be two independent, $\fn_jvn \100dpi \inline d$-dimensional sub-fractional Brownian motions with respective indices $\fn_jvn \100dpi \inline H_i\in(0,1)$. Assume $\fn_jvn \100dpi \inline d\geq 2$. Our principal results are the necessary and sufficient condition for the existence and smoothness of the collision local time and the intersection local time of $\fn_jvn \100dpi \inline S^{H_1}$ and $\fn_jvn \100dpi \inline S^{H_2}$ through chaos expansion and elementary inequalities. 2015 Vol. 31 (5): 547-560 [Abstract] ( 281 ) [HTML 1KB] [ PDF 442KB] ( 611 )

 News

 ·
 ·
 ·
 · New and modified homepage for APS comes