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.

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.

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.

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  and decides to buy a reinsurance contract written on the total
claim amounts basis, i.e. the reinsurer covers  and the cedent covers
. In addition, the insurer is obligated to compensate the reinsurer
for undertaking the risk by paying the reinsurance premium, 
( 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.

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.

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.

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.

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  and
denote the smallest order statistics among ,  and ,
respectively, where and . We then prove that $
and  are ordered in terms of the usual stochastic order,
hazard rate order and likelihood ratio order under the majorization relationship
between  and .