Mathematical And Statistical Methods In Insurance And by Andras Kornai

By Andras Kornai

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Extra resources for Mathematical And Statistical Methods In Insurance And Finance

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For a more detailed discussion on these results see [DGKR03]. In the reduction algorithm proposed by [GKHR03], only the information on the probability of the deleted scenarios survives, through an optimal redistribution rule, while the information related to the values in the deleted nodes disappears. Starting from the method described in [GKHR03], in this contribution we propose an aggregation algorithm in which we keep trace not only of the probabilities of the deleted scenarios, but also of the values of the deleted nodes.

Then in Section 4 the attention is focused on the problem of characterizing risks for which the gap between Bounds for Concave Distortion Risk Measures for Sums of Risks 45 bounds of risk measures is maximum or minimum. Some concluding remarks in Section 5 end the paper. 2 The Class of Distortion Risk Measures As it is well known, an insurance risk is defined as a non-negative real-valued random variable X defined on some probability space. Here we consider a set Ŵ of risks with bounded support [0, c].

A typical example is given by the multi-period two-stage decision problem which represents a convenient form used to recast multi-stage stochastic programs. , there is no correspondence between time periods and decision stages. , by decreasing the number of realizations for the random quantities. These two strategies can be jointly applied to obtain a substantial reduction in the original scenario tree. In [K98] an application of time and state aggregations to built arbitrage-free scenario trees is presented.

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