Let Xi:n denote the ith-order statistic of a random sample of size n from a continuous distribution with distribution function F. It is shown that if F is a decreasing failure rate (DFR) distribution, then Xi:n is less dispersed than Xj:m for i[less-than-or-equals, slant]j and...

In this paper we establish some stochastic ordering results among residual record values in two sample problems. We also discuss some applications.

Let (Xi, Yi) i=1, 2, ..., n be n independent and identically distributed random variables from some continuous bivariate distribution. If X(r) denotes the rth ordered X-variate then the Y-variate, Y[r], paired with X(r) is called the concomitant of the rth order statistic. In this...

In this paper we establish multivariate hazard rate, multivariate reverse hazard rate, and multivariate likelihood ratio stochastic orderings among multivariate random mapping (mixture) distributions. The new results streamline and simplify the proofs of some partial results that have recently...

This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated...

The paper derives many existing risk measures and premium principles by minimizing a Markow bound for the tail probability. Our approach involves two exogenous functions v(S) and ... Minimizing a general Markow bound leads to the following unifying equation. [Marc J. Goovaerts, Rob Kaas, Jan...

In arbitrage-free but incomplete markets, the equivalent martingale measure Q for pricing traded assets is not uniquely determined. A possible approach when it comes to choosing a particular pricing measure is to consider the one that is 'closest'to the physical probability measure P, where...

Premiums and benefits associated with traditional life insurance contracts are usually specified as fixed amounts in policy conditions. However, reserve-dependent surrender values and reserve-dependent expenses are common in insurance practice. The famous Cantelli theorem in life insurance...

In this paper, we introduce two classes of indices which can be used to measure the market perception concerning the degree of dependency that exists between a set of random variables, representing different stock prices at a xed future date. The construction of these measures is based on the...

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed bene ts. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so...