For any positive integers m and n, let X1,X2,...,Xm[logical or]n be independent random variables with possibly nonidentical distributions. Let X1:n<=X2:n<=...<=Xn:n be order statistics of random variables X1,X2,...,Xn, and let X1:m<=X2:m<=...<=Xm:m be order statistics of random variables X1,X2,...,Xm. It is shown that (Xj:n,Xj+1:n,...,Xn:n) given Xi:m>y for j-i=max{n-m,0}, and (X1:n,X2:n,...,Xj:n) given Xi:m=y for j-i=min{n-m,0} are all increasing in y with respect to the usual multivariate...</=x2:n<=...<=xn:n>

In this note, we consider the dependent default risk model of factor type. The dependence between the returns of assets is driven by default indicators. Sufficient conditions on the dependence structure of default indicators and on the utility function are investigated which enable one to order...

In the literature, orderings of optimal allocations of policy limits and deductibles were established by maximizing the expected utility of wealth of the policyholder. In this paper, by applying the bivariate characterizations of stochastic ordering relations, we reconsider the same model and...

The Lp-metric Δh,p(X) between the survival function F¯ of a random variable X and its distortion h∘F¯ is a characteristic of the variability of X. In this paper, it is shown that if a random variable X is larger than another random variable Y in the location-independent risk order or in the...

The tail distortion risk measure at level p∈(0,1) was introduced in  Zhu and Li (2012) and  Yang (2012), where the parameter p represents the confidence level. In this paper, we establish the second-order asymptotics of the risk concentration based on the tail distortion risk measure, as...