Upper and lower bounds for sums of random variables

By Rob Kaas, Jan Dhaene, Marc J. Goovaerts. 2000

237 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2ab309f27853f3447fc323507e1e8e64c9ff7731

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In Finance

In Management Science and Operations Research

Citations in the corpus

The Concept of Comonotonicity in Actuarial Science and Finance: Applications (2002, unknown): “and V ar [Y | Λ = λ] = σ(2)Y ( 1 − r (Y,Λ)2) , (12) where r (Y,Λ) is Pearson’s correlation coefficient for the couple (Y,Λ).”
Optimal approximations for risk measures of sums of lognormals based on conditional expectations (2008, background): “From Jensen’s inequality one can prove that S is smaller in convex order than S: S ≤cx S, (19) which means that for any convex function v(x) it holds that E[v(S)] ≤ E[v(S)], (20) provided the expectations exist.”
Risk Measures and Comonotonicity: A Review (2006, unknown): “[17].”
Risk aggregation with dependence uncertainty (2014, methodology): “For example, using the Gaussian multivariate copula can result in severely underestimating probability of simultaneous default in a large basket of firms (McNeil et al. (2005)).”
Pricing of arithmetic basket options by conditioning (2004, unknown): “, Xn). More precisely, we assume that there exists some random variable Λ with a given distribution function, such that we know the conditional distribution, given Λ = λ, of the random variables Xi, for all possible values of λ. We recall from Kaas et al. (2000) that a lower bound, in the sense of”
The concept of comonotonicity in actuarial science and finance: theory (2002, unknown): “Definition 5 The random vector X has marginal cdf ’s FXi that belong to the same location-scale family of distributions, if there exist a random variable Y , positive real constants ai and real constants bi such that the relation Xi d = aiY + bi (30)”
Value-at-Risk Bounds with Variance Constraints (2015, unknown): “Primarily, in the context of lognormal risks, Kaas et al. (2000) show that portfolio sums can be closely “approximated” by taking the appropriate conditional expectation.”
Does positive dependence between individual risks increase stop-loss premiums? (2001, background): “Dhaene, Wang, Young and Goovaerts (2000), Goovaerts, Dhaene and De Schepper (2000), Kaas, Dhaene and Goovaerts (2000) , Simon, Goovaerts and Dhaene (2000), Vyncke, Goovaerts and Dhaene (2000) as well as the references therein.”
A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum (2002, unknown): “Proofs for the special case n = 2 and for the individual life model (two-point distributions) are to be found in Dhaene & Goovaerts (1996) and Dhaene & Goovaerts (1997) respectively.”
Bounds for the price of discrete arithmetic Asian options (2006, methodology): “Based on Kaas et al. (2000), we chooseS := Su, with S u = F−1X1|Λ(U) + F −1 X2|Λ(U) + · · · + F−1Xn|Λ(U).”
Dependence in Dempster-Shafer theory and probability bounds analysis* (2004, background): “Methods that seem to do this are implicitly assuming some copula family that takes the correlation and specifies a particular dependence function. This section shows how the theory of copula can be used directly and explicitly to compute arithmetic functions between the variables with arbitrarily co”