arXiv subjects

Chuancun Yin

Publications and source records attributed to Chuancun Yin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Doubly truncated moment risk measures for elliptical distributions

In this paper, we define doubly truncated moment (DTM), doubly truncated skewness (DTS) and kurtosis (DTK). We derive DTM formulae for elliptical family, with emphasis on normal, student-$t$, logistic, Laplace and Pearson type VII distributions. We also present explicit formulas of the DTE (doubly truncated expectation), DTV (doubly truncated variance), DTS and DTK for those distributions. As illustrative example, DTEs, DTVs, DTSs and DTKs of three industry segments' (Banks, Insurance, Financial and Credit Service) stock return in London stock exchange are discussed.

math.ST↗

arXiv2021

Multivariate double truncated expectation and covariance risk measures for elliptical distributions

The main objective of this work is to calculate the multivariate double truncated expectation (MDTE) and covariance (MDTCov) for elliptical distributions. We also consider double truncated expectation (DTE) and variance (DTV) for univariate elliptical distributions. The exact expressions of MDTE and MDTCov are derived for some special cases of the family, such as normal, student-$t$, logistic, Laplace and Pearson type VII distributions. As numerical illustration, the DTE, DTV, MDTE and MDTCov for normal distribution are computed in details. Finally, we discuss MDTE and MDTCov of three industry segments' (Banks, Insurance, Financial and Credit Service) stock return in London stock exchange.

math.ST↗

arXiv2021

An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normalDistribution with Applications to Associated Stochastic Orderings

We establish an identity for E f (Y) -E f (X), when X and Y both have matrix variateskew-normal distributions and the function f fulfills some weak conditions. Thecharacteristic function of matrix variate skew normal distribution is then derived. Finally,we make use of it to derive some necessary and sucient conditions for the comparisonof matrix variate skew-normal distributions under six di erent orders, such as usualstochastic order, convex order, increasing convex order, upper orthant order,directionally convex order and supermodular order.

math.ST↗

arXiv2021

Multivariate tail covariance for generalized skew-elliptical distributions

In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized skew-logistic and generalized skew-Laplace distributions, are also considered. In order to test the theoretical feasibility of our results, the MTCov for skewed and non skewed normal distributions are computed and compared. Finally, we give a special formula of the MTCov for generalized skew-elliptical distributions.

q-fin.RM↗

arXiv2020

Explicit expressions for joint moments of $n$-dimensional elliptical distributions

Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive $E[X_{1}^{2}f(\mathbf{X})]$ for any measurable function $f$ satisfying some regularity conditions. Then, by applying this result, we obtain new formulae for expectations of product of normally distributed random variables, and also present simplified expressions of $E[X_{1}^{2}f(\mathbf{X})]$ for multivariate Student-$t$, logistic and Laplace distributions.

math.ST↗

arXiv2020

A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal distributions, conditional distributions, linear transformations, characteristic functions and dependence measure in the perspective of the inconsistency property. In addition, we provide a real data example to show that the new distributions have reasonable flexibility.

math.ST↗

arXiv2020

Conditional tail risk expectations for location-scale mixture of elliptical distributions

We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student-$t$ distributions, location-scale mixture of Logistic distributions and location-scale mixture of Laplace distributions. We also consider portfolio risk decomposition with TCE for location-scale mixture of elliptical distributions.

math.ST↗

arXiv2019

Stochastic Orderings of Multivariate Elliptical Distributions

Let ${\bf X}$ and ${\bf X}$ be two $n$-dimensional elliptical random vectors, we establish an identity for $E[f({\bf Y})]-E[f({\bf X})]$, where $f: \Bbb{R}^n \rightarrow \Bbb{R}$ fulfilling some regularity conditions. Using this identity we provide a unified derivation of sufficient and necessary conditions for classifying multivariate elliptical random vectors according to several main integral stochastic orders. As a consequence we obtain new inequalities by applying it to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.

math.ST↗

arXiv2019

The $CI$-index: a new index to characterize the scientific output of researchers

We propose a simple new index, named the $CI$-index, based on the Choquet integral to characterize the scientific output of researchers. This index is an improvement of the $A$-index and $R$-index and has a notable feature that highly cited papers have highly weights and lowly cited papers have lowly weights. In applications many researchers may have the same $h$-index, $g$-index or $R$-index. The $CI$-index can be provided an effective method of distinguish among such researchers.

stat.AP↗

arXiv2019

Representations of the Riemann zeta function: A probabilistic approach

In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at fractional points by means of probabilistic approach. The proof is based on the moment generating function and the characteristic function of logistic and half-logistic distributions in probability theory.

math.PR↗

arXiv2018

A New Class of Symmetric Distributions Including the Elliptically Symmetric Logistic

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied, including the distribution of linear transformations, marginal distributions, conditional distributions, moments, stochastic representations and characteristic function.

math.PR↗

arXiv2018

Elliptical Distributions-Based Weights-Determining Method for OWA Operators

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers' choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the RIM quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.

cs.AI↗

arXiv2018

A unifying approach to constrained and unconstrained optimal reinsurance

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a distortion premium principle. Firstly, we show that how optimal reinsurance models for the unconstrained optimization problem and constrained optimization problems can be formulated in a unified way. Secondly, we propose a geometric approach to solve optimal reinsurance problems directly. This paper considers a class of increasing convex ceded loss functions and derives the explicit solutions of the optimal reinsurance which can be in forms of quota-share, stop-loss, change-loss, the combination of quota-share and change-loss or the combination of change-loss and change-loss with different retentions. Finally, we consider two specific cases: Value at Risk (VaR) and Tail Value at Risk (TVaR).

q-fin.RM↗

arXiv2016

On the last exit times for spectrally negative Lévy processes

Using a new approach, for spectrally negative Lévy processes we find joint Laplace transforms involving the last exit time (from a semi-infinite interval), the value of the process at the last exit time and the associated occupation time, which generalizes some previous results.

math.PR↗

arXiv2016

Sharp convex bounds on the aggregate sums--An alternative proof

It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32, 71-80. Cheung (2010), Characterizing a comonotonic random vector by the distribution of the sum of its components, Insurance: Mathematics and Economics 47(2), 130-136] and that a random vector with given marginal distributions is mutually exclusive if and only if it has the minimal convex sum [Cheung and Lo (2014), Characterizing mutual exclusivity as the strongest negative multivariate dependence structure, Insurance: Mathematics and Economics 55, 180-190]. In this note, we give a new proof of this two results using the theories of distortion risk measure and expected utility.

q-fin.RM↗

arXiv2016

New class of distortion risk measures and their tail asymptotics with emphasis on VaR

Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the composting methods, the mixing methods and the approach that based on the theory of copula. Subadditivity is an important property when aggregating risks in order to preserve the benefits of diversification. However, Value at risk (VaR), as the most well-known example of distortion risk measure is not always globally subadditive, except of elliptically distributed risks. In this paper, instead of study subadditivity we investigate the tail subadditivity for VaR and other distortion risk measures. In particular, we demonstrate that VaR is tail subadditive for the case where the support of risk is bounded. Various examples are also presented to illustrate the results.

q-fin.RM↗

arXiv2015

Remarks on equality of two distributions under some partial orders

In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.

q-fin.RM↗

arXiv2014

A new multivariate dependence measure based on comonotonicity

In this paper we introduce a new multivariate dependence measure based on comonotonicity by means of product moment which motivated by the recent papers of Koch and Schepper (ASTIN Bulletin 41 (2011) 191-213) and Dhaene et al. (Journal of Computational and Applied Mathematics 263 (2014) 78-87). Some differences and relations between the new dependence measure and other multivariate measures are an- alyzed. We also give several characteristics of this measure and estimations based on the definitions and its property are presented.

q-fin.RM↗