Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes (X i , Y i ), i ≥ 1 and a claim counting random variable N . In this paper we are concerned with the joint distribution function F of the largest claim sizes (X N :N , Y N :N ). By allowing N to depend on some parameter, say θ, then F = F (θ) is for various choices of N a tractable parametric family of bivariate distribution functions. We investigate both distributional and extremal properties of (X N :N , Y N :N ). Furthermore, we present several applications of the implied parametric models to some data from the literature and a new data set from a Swiss insurance company 1 .
Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely a) construction of an optimal renewal tariff subject to business and technical constraints, and b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic sub-optimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.
Consider two different portfolios which have claims triggered by the same events. Their corresponding collective model over a fixed time period is given in terms of individual claim sizes (X i , Y i), i ≥ 1 and a claim counting random variable N. In this paper we are concerned with the joint distribution function F of the largest claim sizes (X N :N , Y N :N). By allowing N to depend on some parameter, say θ, then F = F (θ) is for various choices of N a tractable parametric family of bivariate distribution functions. We investigate both distributional and extremal properties of (X N :N , Y N :N). Furthermore, we present several applications of the implied parametric models to some data from the literature and a new data set from a Swiss insurance company 1 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.