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Actuarial Theory for Dependent Risks: Measures, Orders and Models
TL;DR: In this article, the authors provide an essential guide to managing modern financial risk by combining coverage of stochastic order and risk measure theories with the basics of risk management, including dependence concepts and dependence orderings.
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Decision theoretic foundations of credibility theory
TL;DR: An approach to premium calculation based on loss functions is introduced, and credibility formulas for the resulting premium principles are derived, and these formulas turn out to be Bayes rules in the sense of statistical decision theory.
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A comonotonic image of independence for additive risk measures
TL;DR: A new axiomatic characterization of risk measures that are additive for independent random variables that includes an axiom that guarantees monotonicity of the risk measure and the axiom of additivity for comonotonic random variables is presented.
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On some properties of a class of multivariate erlang mixtures with insurance applications
Gordon E. Willmot,Jae-Kyung Woo +1 more
TL;DR: In this paper, a class of multivariate mixed Erlang distributions with different scale parameters is discussed and various distributional properties related to applications in insurance risk theory are derived, allowing for the study of stop-loss moments, premium calculation, and the risk allocation problem.
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Properties of the Esscher premium calculation principle
TL;DR: In this paper, order preserving and order inducing properties of the Escher premium calculation principle are investigated, and it is found that using this principle higher premiums might be asked for smaller risks, and also for less variable risks.