On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies

Ribas, Carme Besson; Marín-Solano, Jesús; Alegre, A.

doi:10.1016/s0167-6687(02)00210-x

Cited by 7 publications

(3 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, an accident involving a tourist group, life insurance for a husband and wife or pensions for workers of the same company are likely to produce dependent risks. For discussion of the dependence of risks and further examples, see [10,16] and [26].…”

Section: Applications Of Markov Binomial Modelsmentioning

confidence: 99%

Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Čekanavičius¹,

Vellaisamy²

2010

Bernoulli

View full text Add to dashboard Cite

Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are calculated. For the upper bounds, the smoothing properties of compound Poisson distributions are applied. For the lower bound estimates, the characteristic function method is used.

show abstract

Section: Applications Of Markov Binomial Modelsmentioning

confidence: 99%

Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Čekanavičius¹,

Vellaisamy²

2010

Bernoulli

View full text Add to dashboard Cite

show abstract

“…This assumption is relaxed in Ribas, Marín-Solano, Alegre [28] , where bivariate dependencies are taken into account.…”

Section: Final Remarksmentioning

confidence: 99%

Recursions for the Individual Risk Model

Dhaene

Ribas

Vernic

2006

Acta Math. Appl. Sin, Engl. Ser.

View full text Add to dashboard Cite

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.

show abstract

“…Research results show that comonotonicity had been a extreme case of dependency between random variables (see. Dhaene J. et al [3], [4], [5], Ribas C. [8]). Thus, for example, comonotonicity between lives in a group implies a special characteristics of the group-life that one member of the group attains venerable age then all of other members of the group also attain venerable age.…”

Section: Introductionmentioning

confidence: 99%

Modelling comonotonic group-life under dependent decrement causes

Wang

2011

Preprint

View full text Add to dashboard Cite

Comonotonicity had been a extreme case of dependency between random variables. This article consider an extension of single life model under multiple dependent decrement causes to the case of comonotonic group-life. * The research has been supported by the scientific foundation 2006, No.62033 of Guangzhou Education Bureau.1 the copula functions. A statistical estimation on the net survival functions using the observations of crude survivals was proposed. Wang et al.(2009) [10] has considered the decrement model for comonotonic group-life with status of joint-survival and last survival under independent multiple decrement causes.The distribution model with statistical analysis on comonotonic group-life under multiple dependent decrement causes will be considered in the present paper.The comonotonicity properties seemingly make that each group-life can be represented by any single member of the group, which would leads to a simple way inducing a joint distribution for the considered collection of comonotonic grouplife. This paper is organized as follows. In Section 2, the main concepts like comonotonicity, copula functions, survival function as well as some useful obtained results are mentioned. in Section 3, we construct a model for dependent multiple comonotonic group-life. PreliminariesDefinition 2.1 (Dhaene J.[3]) Let R n be a n-dimensional Euclidean space, A ⊂ R n is said to be a comonotonic vectors set if for any vectors x, y ∈ A, it holds that x y or x y. Where x ( )y means that x i ( )y i , i = 1, . . . , n.Following [3], we see that the earlier concept of two comonotonic random variables due to Schmeidler (1986), Yarri(1987) 's work on economics. Let (X, Y ) be a two dimensional random vector on the probability space (Ω, F , P ). If for any ω 1 , ω 2 ∈ Ω there always holds that(X(ω 1 )− X(ω 2 ))(Y (ω 1 )− Y (ω 2 )) 0, then, (X, Y ) is said to be comonotonic, this definition was weaken as (X(ω 1 ) − X(ω 2 ))(Y (ω 1 ) − Y (ω 2 )) 0, P.a.s. around 1997. For a n-dimensional random vector X = (X 1 , . . . , X n ) defined on (Ω, F , P ), if there exists a subset A ⊂ R n such that P (X ∈ A) = 1, then A is said to be a support of X. A Random vector X = (X 1 , . . . , X n ) is said to be comonotonic if its support is comonotonic.ability space (Ω, F , P ) is comonotonic if and only if the following equivalent conditions hold:(1) X has a comonotonic support;(2)For all values of X, x = (x 1 , • • • , x n ), the joint distribution of X is F X (x) = min{F X1 (x 1 ), F X2 (x 2 ), . . . , F Xn (x n )};

show abstract

On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies

Cited by 7 publications

References 19 publications

Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Recursions for the Individual Risk Model

Modelling comonotonic group-life under dependent decrement causes

Contact Info

Product

Resources

About