The concept of comonotonicity in actuarial science and finance: theory

By Jan Dhaene, Michel Denuit, Marc J. Goovaerts, Rob Kaas, David Vyncke. Insurance, Mathematics & Economics, 2002

683 citations recorded by the source corpus.

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 certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/9d3dd3e4b90d5136585245c196be3fab6eb13118

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Citations in the corpus

Pareto-Optimal Reinsurance Arrangements Under General Model Settings (2017, neutral): “See Dhaene et al. (2002) for an overview on comonotonicity.”
Optimal Reinsurance with General Premium Principles (2013, neutral): “Another important property associated with V aRα(X) is that for any continuous increasing function φ, we have (see Theorem 1 in Dhaene et al. (2002))”
Lectures on modern convex optimization - analysis, algorithms, and engineering applications (2001, result): “This result offers an alternative (and simpler) proof for the following remarkable fact established by Dhaene et al [10]: if f is a convex function on the axis and η1, .”
Risk Measures and Comonotonicity: A Review (2006, neutral): “[8].”
Self Exciting Threshold Interest Rates Models (2006, methodology): “The spectral representation (14) separates the time and space dependencies of the transition density p(t; x, y) and enables efficient implementation of stochastic volatility by random changes in time just as Carr and Wu (2004) for option pricing under Lévy models.”
Comonotonic Approximations for Optimal Portfolio Selection Problems (2005, background): “i=0 CTEp [Xi] , provided all FXi are continuous, (12)”
Copula Theory: An Introduction (2010, neutral): “This concept has several important consequences in applications, as described in [38, 39].”
Bounds for the price of discrete arithmetic Asian options (2006, neutral): “We also show in Section 2.3 how to sharpen the improved comonotonic upper bound of Kaas et al. (2000) and Dhaene et al. (2002a) by obtaining another so-called partially exact/comonotonic upper bound which consists of an exact part of the option price and some improved comonotonic upper bound for…”
Some New Classes of Consistent Risk Measures (2004, background): “That is the reason why we called it Orlicz risk measure in Haezendonck and Goovaerts (1982). The idea originates from the Swiss premium calculation principle due to Bühlmann (1977) .”
After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures (2006, neutral): “Comonotonicity approaches (e.g., Dhaene et al., 2003a, b): These apply to situations where we are interested in the sums of random variables and cannot plausibly assume that these random variables are independent.”
General closed-form basket option pricing bounds (2016, neutral): “The newly introduced basket involves the components of the comonotonic version of the original random vector, see for example Dhaene et al. (2002b) and Dhaene et al. (2002a).”