Modelling random vectors of dependent risks with different elliptical components

In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.

Use of phenytoin, phenobarbital carbamazepine, levetiracetam lamotrigine and valproate in pregnancy and breastfeeding: risk of major malformations, dose-dependency, monotherapy vs polytherapy, pharmacokinetics and clinical implications

: It is challenging to balance the fetal risks associated with the use of antiepileptic drugs (AEDs) against maternal and fetal risks of seizure worsening and therefore it is very important to define and distinguish the possible risks entailed by different AEDs. This paper aims to undertake a comprehensive review regarding the possible risks of four classical (phenytoin, carbamazepine, phenobarbital and valproate) and two newer (lamotrigine and levetiracetam) AEDs during pregnancy. The review focuses on major and organ-specific malformations, dose-dependent risks, mono vs polytherapy, and clinical pharmacokinetics. A discussion regarding the safety of AED use during breastfeeding is also provided.

COPULA REPRESENTATIONS FOR THE SUM OF DEPENDENT RISKS: MODELS AND COMPARISONS

The study of the distributions of sums of dependent risks is a key topic in actuarial sciences, risk management, reliability and in many branches of applied and theoretical probability. However, there are few results where the distribution of the sum of dependent random variables is available in a closed form. In this paper, we obtain several analytical expressions for the distribution of the aggregated risks under dependence in terms of copulas. We provide several representations based on the underlying copula and the marginal distribution functions under general hypotheses and in any dimension. Then, we study stochastic comparisons between sums of dependent risks. Finally, we illustrate our theoretical results by studying some specific models obtained from Clayton, Ali-Mikhail-Haq and Farlie-Gumbel-Morgenstern copulas. Extensions to more general copulas are also included. Bounds and the limiting behavior of the hazard rate function for the aggregated distribution of some copulas are studied as well.

How correlation risk in basket credit derivatives might be priced and managed?

In this paper, we construct quantitative models in which the dependence structure of the firms’ default times is incorporated. Such models serve as the underlying frameworks in our proposed approach to price and hedge basket credit derivatives. Through the Gaussian copula-based method, we model the default correlation risk and develop valuation formulas for credit derivatives. Using single-name derivatives in a hedging strategy for basket credit derivatives, the utility of the delta and delta-gamma hedging techniques are examined. This enables the management of risk attributed to the changes in correlation without the need for a large number of hedging instruments. Our research contributions provide insights on how dependent risks in basket credit derivatives could be dealt with effectively.