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 2017 Vol.33 Issue.3,Published 2017-07-07 article
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 221 LAD Estimation for Linear Regression Models with Contaminated Data YE Peng; ZHOU XiuQing In this paper, linear regression models with contaminated data are considered. Estimation methods for the regression parameters based on least absolute deviations (LAD) are proposed, and properties of consistency and asymptotic normality of the proposed method are proved under some regular conditions. Simulations are done to assess the properties of the method when sample size is small, and simulation results show that the methods works well. 2017 Vol. 33 (3): 221-231 [Abstract] ( 179 ) [HTML 1KB] [ PDF 583KB] ( 459 )
 232 Market-Dependent Casuality Between Futures and Spot LIN Lu, SHEN Wei, ZHANG Yan, LIANG LuFang, ZHANG ChuanGang The relationship between futures and spot is still an important issue in academic communities and supervisory departments. In this paper, the Granger Causality Test is extended into quantile regression and then the relationship between futures and spot is investigated at different quantile positions. Note that under the model with differential data, different quantile positions are related to the corresponding financial environments. Consequently, a market-dependent casuality between futures and spot is established, by which we can study the relationship more deeply and comprehensively. The main points of view obtained in this paper are what follows: 1. The relationship between futures and spot is strongly related to the financial environments, besides the features of futures and spot; 2. Under the normal and stable financial markets, there is casuality one another, but the relationship will be abnormal under extremal financial conditions, the common relationship between futures and spot is masked by other financial factors; 3. If the casuality was seen as a normal fact logically, then the abnormal relationship should indicate a bad or extremal financial environment, which provides supervisory departments with a warning signal. 2017 Vol. 33 (3): 232-246 [Abstract] ( 165 ) [HTML 1KB] [ PDF 849KB] ( 464 )
 247 The Study of Default Probability under Incomplete Information Based on Structural Model LI XiuQiong, CHEN ShaoGang This paper establish a first passage time model based on the Merton's structural model by using the method of geometric Brownian motion. In this paper, we consider the accounting noise and historical default record and then introduce a new incomplete information hypothesis. Besides, we introduce the stock's liquidity value into the model, and apply its method measurement which based on Merton's structural model to the first passage time model to obtain the endogenous default boundary. Based on the incomplete information, the conditional default probability is derived by using the default boundary. And at the last of this passage, we analysis the effect of the correlation between stock's price and company assets on the default probability. 2017 Vol. 33 (3): 247-256 [Abstract] ( 165 ) [HTML 1KB] [ PDF 651KB] ( 382 )
 257 Exact Asymptotics in Complete Moment Convergence KONG LingTao, DAI HongShuai Let $\fn_jvn \100dpi \inline \{X_n,n\geq 1\}$  be a sequence of i.i.d. random variables with absolutely continuous distribution function. Denote the record times and the associated counting process of $\fn_jvn \100dpi \inline \{X_n,n\geq 1\}$by $\fn_jvn \100dpi \inline \{L(n),n\geq 1\}$and $\fn_jvn \100dpi \inline \{\mu(n),n\geq 1\}$, respectively. In this paper, we obtain the exact asymptotics in complete moment convergence of $\fn_jvn \100dpi \inline \{L(n),n\geq 1\}$ and $\fn_jvn \100dpi \inline \{\mu(n),n\geq 1\}$. 2017 Vol. 33 (3): 257-266 [Abstract] ( 152 ) [HTML 1KB] [ PDF 445KB] ( 428 )
 267 Optimal Reinsurance under GlueVaR Distortion Risk Measures WANG WenYuan, XIAO LiQun Motivated by [1] and [2], we study in this paper the optimal (from the insurer's point of view) reinsurance problem when risk is measured by a general risk measure, namely the GlueVaR distortion risk measures which is firstly proposed by [3].Suppose an insurer is exposed to the risk $\fn_jvn \100dpi \inline X$ and decides to buy a reinsurance contract written on the total claim amounts basis, i.e. the reinsurer covers $\fn_jvn \100dpi \inline f(X)$ and the cedent covers $\fn_jvn \100dpi \inline X-f(X)$. In addition, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium, $\fn_jvn \100dpi \inline (1+\rho)\ep[f(X)]$ ($\fn_jvn \100dpi \inline \rho$ is the safety loading), under the expectation premium principle. Based on a technique used in [2], this paper derives the optimal ceded loss functions in a class of increasing convex ceded loss functions. It turns out that the optimal ceded loss function is of stop-loss type. 2017 Vol. 33 (3): 267-284 [Abstract] ( 202 ) [HTML 1KB] [ PDF 482KB] ( 551 )
 285 Valuation of CatEPuts with Regime Switching CHENG GongPin, FAN Kun This paper investigates the pricing of CatEPuts under a Markovian regime-switching jump-diffusion model. The parameters of this model, including the risk-free interest rate, the appreciation rate and the volatility of the clients' equity, are modulated by a continuous-time, finite-state, observable Markov chain. An equivalent martingale measure is selected by employing the regime-switching Esscher transform. The fast Fourier transform (FFT) technique is applied to price the CatEPuts. In a two-state Markov chain case, numerical example is presented to illustrate the practical implementation of the model. 2017 Vol. 33 (3): 285-296 [Abstract] ( 171 ) [HTML 1KB] [ PDF 1198KB] ( 458 )
 297 Stochastic Averaging for Non-Lipschitz SDEs with G-Brownian Motion HAN Min, LIU YaXiang This paper concerns stochastic differential equations driven by G-Brownian motion under non-Lipschitz condition which is a much weaker condition with a wider range of applications. Stochastic averaging is established for such non-Lipschitz SDEs where an averaged system is presented to replace the original one in the sense of mean square. An example is presented to illustrate the averaging principle. 2017 Vol. 33 (3): 297-309 [Abstract] ( 166 ) [HTML 1KB] [ PDF 475KB] ( 624 )
 310 Approximated Maximum Likelihood Estimator for Frechet Distribution under Type II Censoring ZENG LinRui, TANG YinCai, DOU Wen Frechet distribution is an important life distribution. In this paper, approximated maximum likelihood estimator for two parameter Frechet distribution under type II censoring is investigated. And the feasibility of this method is obtained through the Monto-Carlo simulation. 2017 Vol. 33 (3): 310-316 [Abstract] ( 174 ) [HTML 1KB] [ PDF 493KB] ( 415 )
 317 Ordering Properties of Minima from Multiple-Outlier Models CHENG MeiFang, FANG LongXiang, YANG Fang $\fn_jvn \100dpi \inline X_{p+1},\ldots,X_n$In this paper, we compare the smallest order statistics arising from multiple-outlier models when the numbers of independent and identically distributed random variables are different. Let $\fn_jvn \100dpi \inline X_{1:n}(p,q)$ and $\fn_jvn \100dpi \inline X_{1:n^*}(p^*,q^*)$ denote the smallest order statistics among $\fn_jvn \100dpi \inline X_1,\ldots,X_p$, $\fn_jvn \100dpi \inline X_{p+1},\ldots,X_n$ and $\fn_jvn \100dpi \inline X_1,\ldots,X_{p^*},X_{p^*+1},\ldots, X_{n^*}$, respectively, where $\fn_jvn \100dpi \inline q=n-p$and $\fn_jvn \100dpi \inline q^*=n^*-p^*$. We then prove that \$$\fn_jvn \100dpi \inline X_{1:n}(p,q)$ and $\fn_jvn \100dpi \inline X_{1:n^*}(p^*,q^*)$ are ordered in terms of the usual stochastic order, hazard rate order and likelihood ratio order under the majorization relationship between $\fn_jvn \100dpi \inline (p,q)$ and $\fn_jvn \100dpi \inline (p^*,q^*)$. 2017 Vol. 33 (3): 317-330 [Abstract] ( 159 ) [HTML 1KB] [ PDF 479KB] ( 493 )

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