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Summary
We employ the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for common events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov processes theory. Since the claim intensity is not observable we employ state estimation on the basis of the number of claims i.e. we obtain the Kalman-Bucy filter. In order to use the Kalman-Bucy filter, the claim arrival process (i.e. the Cox process) and the claim intensity (i.e. the shot noise process) should be transformed and approximated to two-dimensional Gaussian process. Based on this filter, we derive reserving formulae at any time for common events with and without stop-loss reinsurance contract. We also examine the effect on reserves caused by change in the values of the security loading and the retention limit. |
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Ji-Wook Jang obtained his B.A. in Business Administration from Sogang University, Seoul in 1991. After studying Actuarial Science for Master of Science at the City University, London, he completed his Ph.D. at the London School of Economics and Political Science (‘LSE’) in 1998 in Statistics. Before he started his doctorate with LSE, he went to work for LG Securities International Limited, London in 1994 as an assistant to head trader and the City University, London in 1993 as a researcher for a paper prepared for Scottish Amicable, Glasgow.
After working as a lecturer of statistics (and also part-time teacher during his doctorate) at LSE, Ji-Wook is currently a lecturer of actuarial science at the University of New South Wales, Sydney, Australia.
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