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The concept of comonotonicity in Actuarial Science and Finance: Theory
In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a… Expand
The Concept of Comonotonicity in Actuarial Science and Finance: Applications
In an insurance context, one is often interested in the distribution function of a sum of random variables (rv’s). Such a sum appears when considering the aggregate claims of an insurance portfolio… Expand
Actuarial Theory for Dependent Risks: Measures, Orders and Models
The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be… Expand
Risk Measures and Comonotonicity: A Review
In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special… Expand
Upper and Lower Bounds for Sums of Random Variables.
In this contribution, the upper bounds for sums of dependent random variables X1 + X2 +...+ Xn derived by using comonotonicity are sharpened for the case when there exists a random variable Z such… Expand
Dependency of risks and stop-loss order.
The correlation order, which is defined as a partial order between bivariate distributions with equal marginals, is shown to be a helpfull tool for deriving results concerning the riskiness of portfolios with pairwise dependencies. Expand
Modern Actuarial Risk Theory: Using R
Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model… Expand
Optimal Capital Allocation Principles
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… Expand
Modern Actuarial Risk Theory
Apart from standard actuarial theory, this text contains methods that are relevant for actuarial practice, as well as generalised linear models with an eye on actuarial applications.
Remarks on quantiles and distortion risk measures
Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is essentially true, but that one has to be careful with the correct formulation… Expand