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2015 Vol.31 Issue.4,Published 2015-08-31

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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  with , has been studied in many
literatures. In this paper, we provide some theoretical results of how the shrinkage
rule changing with  under two settings:  and ,
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
-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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