Analytical studies in stop-loss reinsurance. II

Abstract

I

In an earlier paper [5] we discussed the problem of finding an unbiased estimator of where p (x, 0) is a given frequency density and 0 is a (set of) parameter(s). In general, will not be an unbiased estimator of (1), when Ô is an unbiased estimate of O. In [5] it was shown that is an unbiased estimator of (1), if we define y_i , as the larger of 0 and X _j - c. It was emphasized that the resulting estimate may very well be zero, even when it is unreasonable to assume that the premium for a stop.loss reinsurance. defined by a frequency p (x, 0) of claims x and a critical limit c, should be zero when the critical limit has not been exceeded during the n years considered for the determination of the premium.     

Econophysics review: II. Agent-based models

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from the point of view of agent-based modeling. Of the large number of multi-agent-based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioral finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that we discuss extensively here. Second, kinetic theory models designed to explain certain empirical facts concerning wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.     

On heterogeneity in non-life insurance. Part II

Abstract

Extract

While in some linear estimation problems the principle of unbiasedness can be said to be appropriate, we have just seen that in the present context we will have to appeal to other criteria. Let us first consider what we get from the maximum likelihood method. We do not claim any particular optimum property for this estimate of the risk distribution: it seems plausible however that one can prove a large sample result analogous to the classical result on maximum likelihood estimation.