Ragnar Norberg

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The issue of bonus in life insurance is considered in a model framework where the traditional set-up is extended by letting the experience basis (mortality, interest, etc.) be stochastic. A novel definition of the technical surplus on an insurance contract is proposed, and basic principles for its repayment as bonus are discussed. Making the experience(More)
1. The pterostigma of insect wings usually is a pigmented spot close to the leading edge far out on the wing, having a greater mass than an equally large wing piece in adjacent wing regions. 2. In several dragonfly (Odonata) species the position of the spanwise torsion axis of the wings, the mass distribution of the wings, and the position of the chordwise(More)
The ability to fly opens up ecological opportunities but flight mechanics and muscle energetics impose constraints, one of which is that the maximum body size must be kept below a rather low limit. The muscle power available for flight increases in proportion to flight muscle mass and wingbeat frequency. The maximum wingbeat frequency attainable among(More)
We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to(More)
Conditional expected values in Markov chains are solutions to a set of associated backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values,(More)
A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic-demographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First,(More)
Here, we report that on six widely separated Scandinavian islands, the coal tit Parus ater has evolved morphologically in the direction of two absent competitors, the crested tit P. cristatus and the willow tit P.montanus, to the effect that it is up to 10% larger in linear dimensions than conspecifics on the adjacent Swedish mainland, where all three(More)