Actuarial Theory for Dependent Risks: Measures, Orders and Models

By Michel Denuit, Rob Kaas, Goovaerts Marc, Jan Dhaene. 2005

445 citations recorded by the source corpus.

Subfields: Demography, Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/9e8503b2a7f3b60afa47a3977020818a14179df7

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Citations in the corpus

Weighted Risk Capital Allocations (2008, unknown): “…allocation when w does not depend on any cdf is Esscher’s allocation, whose detailed study with further references can be found in, e.g., Bühlmann (1980, 1984), Wang (2002, 2007), Goovaerts et al. (2004), Young (2004), Denuit et al. (2005), Pflug and Römisch (2007) and Goovaerts and Laeven (2008).”
Analysis of ruin measures for the classical compound Poisson risk model with dependence (2010, background): “The reader may consult, e.g. Frees & Valdez (1998), Wang (1998), Bouye et al. (2000), Denuit et al. (2005), and McNeil et al. (2005) for applications of copulas in actuarial science and financial risk management.”
Value-at-Risk Bounds with Variance Constraints (2015, unknown): “In this paper we are interested in finding the minimum possible VaR of the sum m(s2) = inf VaRq(S) (1.2) subject to Xj ∼ Fj, var(S) 6 s2 and the maximum possible VaR (in terms of the upper quantile) M(s2) = supVaR+q (S) (1.3) subject to Xj ∼ Fj, var(S) 6 s2.”
TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts (2012, methodology): “Copulas can be used to construct discrete bivariate distributions as suggested e.g. in Joe (1997) and as illustrated e.g. in Denuit et al. (2005), Cossette et al. (2002), Genest et al. (2003), Trivedi and Zimmer (2005) and Marceau (2009).”
Lower tail dependence for Archimedean copulas: Characterizations and pitfalls (2007, unknown): “Frees and Valdez, 1998; Klugman and Parsa, 1999; Dhaene et al., 2005).”
Optimal Reinsurance Revisited – A Geometric Approach (2010, methodology): “Proof: For fd(x) = (x − d)+ for some d ∈ [0, a], it is readily verified from (7) and (8) that K(fd) = d + (1 + ρ)E(X − d)+ = g(d).”
On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula (2008, background): “The readermay consult e.g. Frees and Valdez (1998), Wang (1998), Bouye et al. (2000), Denuit et al. (2005) and McNeil et al. (2005) for applications of copulas in actuarial science and financial risk management.”
Remarks on quantiles and distortion risk measures (2012, unknown): “Applying Fubini’s theorem to change the order of integration and noticing (2), the second integral in (7) can be transformed into Zþ1”
Worst VaR scenarios with given marginals and measures of association (2009, methodology): “…information (e.g., several moments) on the marginal distributions is available, best-possible lower bounds on P[ψ(X, Y ) < t] can be obtained similarly, by using pointwise best-possible lower bounds on the marginal distributions; see Section 8.4.8 of Denuit et al. (2005) for related results.”
On the construction of copulas and quasi-copulas with given diagonal sections (2008, methodology): “Copulas are used to build models for dependence between risks in financial and actuarial risk management, especially dependence between extreme events (Bäuerle and Müller, 1998; Denuit et al., 2005; Frees and Valdez, 1998; Klugman and Parsa, 1999).”
Convex order and comonotonic conditional mean risk sharing (2012, background): “See, e.g., Denuit et al. (2005).”
Optimal approximations for risk measures of sums of lognormals based on conditional expectations (2008, background): “From (7) and (8), we find that S l can be written as S = n ∑”
SIZE-BIASED TRANSFORM AND CONDITIONAL MEAN RISK SHARING, WITH APPLICATION TO P2P INSURANCE AND TONTINES (2019, background): “This is because the function p → FX̃ ( F−1X (p) ) is convex (see Proposition 3.3.50 in Denuit et al., 2005).”