scholarly journals Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks

2008 ◽  
Vol 38 (1) ◽  
pp. 147-159 ◽  
Author(s):  
Alexandru V. Asimit ◽  
Bruce L. Jones
Keyword(s):  
Dependence Structure ◽  
Tail Probabilities ◽  
Insurance Contracts ◽  
Dependent Risks ◽  
Asymptotic Tail

We consider a dependent portfolio of insurance contracts. Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under certain assumptions about the dependence structure.

scholarly journals Asymptotic Tail Probabilities for Large Claims Reinsurance of a Portfolio of Dependent Risks

2008 ◽  
Vol 38 (01) ◽  
pp. 147-159 ◽  
Author(s):  
Alexandru V. Asimit ◽  
Bruce L. Jones
Keyword(s):  
Dependence Structure ◽  
Tail Probabilities ◽  
Insurance Contracts ◽  
Dependent Risks ◽  
Asymptotic Tail

We consider a dependent portfolio of insurance contracts. Asymptotic tail probabilities of the ECOMOR and LCR reinsurance amounts are obtained under certain assumptions about the dependence structure.

scholarly journals Aggregation of log-linear risks

2014 ◽  
Vol 51 (A) ◽  
pp. 203-212 ◽  
Author(s):  
Paul Embrechts ◽  
Enkelejd Hashorva ◽  
Thomas Mikosch
Keyword(s):  
Stochastic Volatility ◽  
Dependence Structure ◽  
Dimensional Vector ◽  
Tail Behaviour ◽  
Log Normal ◽  
Log Linear ◽  
Asymptotic Tail

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks, we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

Sharp Bounds for Sums of Dependent Risks

2013 ◽  
Vol 50 (01) ◽  
pp. 42-53 ◽  
Author(s):  
Giovanni Puccetti ◽  
Ludger Rüschendorf
Keyword(s):  
Random Variables ◽  
Dependence Structure ◽  
Homogeneous Case ◽  
Marginal Distributions ◽  
Sharp Bounds ◽  
Duality Result ◽  
Dependent Risks ◽  
Monotone Densities ◽  
Monotone Density ◽  
Dual Bounds

Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure have been known since Makarov (1981) and Rüschendorf (1982) for d=2 and, in some examples, for d≥3. Based on a duality result, dual bounds have been introduced in Embrechts and Puccetti (2006b). In the homogeneous case, F 1=···=F n , with monotone density, sharp tail bounds were recently found in Wang and Wang (2011). In this paper we establish the sharpness of the dual bounds in the homogeneous case under general conditions which include, in particular, the case of monotone densities and concave densities. We derive the corresponding optimal couplings and also give an effective method to calculate the sharp bounds.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (03) ◽  
pp. 647-663
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

ASYMPTOTIC BEHAVIOR OF EXTREMAL EVENTS FOR AGGREGATE DEPENDENT RANDOM VARIABLES

2013 ◽  
Vol 27 (4) ◽  
pp. 507-531
Author(s):  
Die Chen ◽  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Value At Risk ◽  
Homogeneous Function ◽  
Individual Risk ◽  
Dependence Structure ◽  
Large Individual ◽  
Tail Behavior ◽  
Large Aggregate ◽  
Dependent Risks ◽  
Aggregate Loss ◽  
The Individual

Consider a portfolio of n identically distributed risks X1, …, Xn with dependence structure modelled by an Archimedean survival copula. It is known that the probability of a large aggregate loss of $\sum\nolimits_{i=1}^{n} X_{i}$ is in proportion to the probability of a large individual loss of X1. The proportionality factor depends on the dependence strength and the tail behavior of the individual risk. In this paper, we establish analogous results for an aggregate loss of the form g(X1, …, Xn) under the more general model in which the Xi's have different but tail-equivalent distributions and the copula remains unchanged, where g is a homogeneous function of order 1. Properties of these factors are studied, and asymptotic Value-at-Risk behaviors of functions of dependent risks are also given. The main results generalize those in Wüthrich [16], Alink, Löwe, and Wüthrich [2], Barbe, Fougères, and Genest [4], and Embrechts, Nešlehová, and Wüthrich [9].

scholarly journals Efficient simulation of tail probabilities of sums of dependent random variables

2011 ◽  
Vol 48 (A) ◽  
pp. 147-164 ◽  
Author(s):  
Jose H. Blanchet ◽  
Leonardo Rojas-Nandayapa
Keyword(s):  
Monte Carlo ◽  
Tail Probability ◽  
Radial Component ◽  
Dependence Structure ◽  
Elliptical Distribution ◽  
Tail Probabilities ◽  
Asymptotically Optimal ◽  
Efficient Simulation ◽  
Financial Options ◽  
Conditional Monte Carlo

We study asymptotically optimal simulation algorithms for approximating the tail probability of P(eX1+⋯+ eXd>u) asu→∞. The first algorithm proposed is based on conditional Monte Carlo and assumes that (X1,…,Xd) has an elliptical distribution with very mild assumptions on the radial component. This algorithm is applicable to a large class of models in finance, as we demonstrate with examples. In addition, we propose an importance sampling algorithm for an arbitrary dependence structure that is shown to be asymptotically optimal under mild assumptions on the marginal distributions and, basically, that we can simulate efficiently (X1,…,Xd|Xj>b) for largeb. Extensions that allow us to handle portfolios of financial options are also discussed.

scholarly journals Economic Capital Allocations for Non-negative Portfolios of Dependent Risks

2008 ◽  
Vol 38 (02) ◽  
pp. 601-619 ◽  
Author(s):  
Edward Furman ◽  
Zinoviy Landsman
Keyword(s):  
General Result ◽  
Economic Capital ◽  
Dependence Structure ◽  
Compound Poisson ◽  
Dependent Risks ◽  
Explicit Expressions

In this paper we explore the problem of economic capital allocations in the context of non-negative multivariate (insurance) risks possessing a dependence structure. We derive a general result and illustrate it with a number of useful examples. One such example, for instance, develops explicit expressions for the discussed economic capital decomposition rule when the underlying portfolio consists of dependent compound Poisson risks.

scholarly journals Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 86 ◽  
Author(s):  
Fouad Marri ◽  
Franck Adékambi ◽  
Khouzeima Moutanabbir
Keyword(s):  
Closed Form ◽  
Exponential Model ◽  
Dependence Structure ◽  
Higher Moments ◽  
Exponential Models ◽  
Dependent Risks ◽  
Aggregate Claims ◽  
Aggregate Amount ◽  
The Impact ◽  
Explicit Expressions

In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims.

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