Rob Kaas

Learn More
In this contribution, the upper bounds for sums of dependent random variables X 1 + X 2 + · · · + X n derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution functions of the X i , given Z = z, are known. By a similar technique, lower bounds are derived. A numerical application for the case(More)
In this paper we investigate approximations for the distribution function of a sum S of lognormal random variables. These approximations are obtained by considering the conditional expectation E[S | Λ ] of S with respect to a conditioning random variable Λ. The choice for Λ is crucial in order to obtain accurate approximations. The different alternatives(More)
We consider the problem of how to determine the required level of the current provision in order to be able to meet a series of future deterministic payment obligations, in case the provision is invested according to a given random return process. Approximate solutions are derived, taking into account imposed minimum levels of the future random values of(More)
Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class(More)
The paper derives many existing risk measures and premium principles by minimizing a Markov bound for the tail probability. Our approach involves two exogenous functions v(S) and ␾(S,p) and another exogenous parameter ␣ ≤ 1. Minimizing a general Markov bound leads to the following unifying equation: ,. z ␣ S vS E E p = ^ ] h g 8 6 B @ For any random(More)
In an insurance context, the discounted sum of losses within a finite or infinite time period can be described as a randomly weighted sum of a sequence of independent random variables. These independent random variables represent the amounts of losses in successive development years, while the weights represent the stochastic discount factors. In this(More)
In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X 1 , X 2 ,. .. , X n) with given marginals has a comonotonic joint distribution, the sum X 1 + X 2 + · · · + X n is the largest possible in convex order. In this note we give a lucid proof of this fact, based on a geometric interpretation of the support(More)