A statistical model to analyse stochastically increasing claims arising out of natural catastrophes is presented. Based on record values, the exponential trends over time can be identified. A more specific three parameter model involving such a trend is also proposed. Observed claims are modeled as a stochastically increasing sequence of Fréchet distributed random variables. The conditions for the consistency and asymptotic normality of the joint maximum likelihood estimator are given. Possible applications in forecasting of claims are indicated. In particular claims data from U.S. hurricanes and Japanese typhoons are discussed. The results are joint with Prof. D. Pfeifer (Germany) and Dr. Yu. Chernikov (Ukraine) and published in Kukush et al. (2004), Extremes 7, 309-336.
Keywords: Natural catastrophe claims; Maximum likelihood estimator; Nevzorov record model; Consistent estimator
Biography: Alexander Kukush is Full Professor of National Taras Shevchenko University of Kyiv. He is elected member of the International Statistical Institute. In 2006 he got Taras Shevchenko Award for a cycle of papers on errors-in-variables regression models, according to decision of Research Council of Kyiv University. He was Visiting Professor or got fellowships at the universities of Belgium, Germany, Seweden, Hungary, Taiwan.
He published more than 100 papers in International mathematical journals. In 2009 he published in Springer the Problem Book on Stochastic Processes and Applications (with 4 co-authors). 7 Ph.D. students defended their theses unider his supervision. His main research interests are Mathematical and Applied Statistics, Financial and Actuarial Mathematics.