Aggregation of Risks and Asymptotic Independence
نویسنده
چکیده
We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of the risks (X, Y ) such that P (X + Y > x) ∼ (const)P (X > x). With the further assumption of non-negativity of the risks, the result is extended to more than two risks. We note a sufficient condition for a distribution to belong to both the maximal domain of attraction of the Gumbel distribution and the subexponential class. We provide examples of distributions which satisfy our assumptions. The examples include cases where the marginal distributions of X and Y are subexponential and also cases where they are not. In addition, the asymptotic behavior of linear combinations of such risks with positive coefficients is explored leading to an approximate solution of an optimization problem which is applied to portfolio design.
منابع مشابه
Independence of an Equivariant and Invariant Functions in Generalized Normal Family
In this paper we explain a necessary and sufficent condition for independence between any arbitrary statistics with sufficient statistics which is also maximum likelihood estimator in a general exponential family with location and scale parameter namely generalized normal distribution. At the end, it is shown that the converse is true except in the asymptotic cases.
متن کاملInterplay of Insurance and Financial Risks with Bivariate Regular Variation
It is known that for an insurer who invests in the financial market, the financial investments may affect its solvency as severely as do insurance claims. This conclusion is usually reached under an assumption of independence or asymptotic independence between insurance risk and financial risk. Such an assumption seems reasonable if the insurer focuses on the traditional insurance business that...
متن کاملParametric Estimation in a Recurrent Competing Risks Model
A resource-efficient approach to making inferences about the distributional properties of the failure times in a competing risks setting is presented. Efficiency is gained by observing recurrences of the compet- ing risks over a random monitoring period. The resulting model is called the recurrent competing risks model (RCRM) and is coupled with two repair strategies whenever the system fails. ...
متن کاملOn the Blocks of Interpoint Distances
We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. We discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. We discuss testing...
متن کاملAggregation of log-linear risks
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.
متن کامل