We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims...

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims...

We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

It is well known that credibility theory in discrete time is closely related to the discrete technique of Kalman filtering. In this paper we show the close relationship between credibility theory and filter theory in discrete and continuous time as well as between credibility theory in a...

In this paper we show how to quantify the uncertainty in the difference between the best estimate for the ultimate claim viewed at the beginning and at the end of one year. A second aspect in this paper is how bootstrapping techniques can be used to simulate these uncertainty for several...

The Munich chain-ladder reserving method was introduced on an axiomatic basis. We analyze these axioms and we define a modified Munich chain-ladder reserving method which is based on an explicit stochastic model. This stochastic model then allows to consider claims prediction and prediction...

We give a rigorous definition of best-estimate reserves for insurance liabilities in a general multiperiod financial market setting. In this general multiperiod financial market setting we describe payoff spaces and optimal dynamic hedging strategies. Based on this optimal dynamic hedging...

It is well known that credibility theory in discrete time is closely related to the discrete technique of Kalman filtering. In this paper we show the close relationship between credibility theory and filter theory in discrete and continuous time as well as between credibility theory in a...

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method...