Kalman-Bucy filtering for linear systems driven by the Cox process with shot noise intensity and its application to the pricing of reinsurance contracts

Angelos Dassios*, J. I Wook Jang

*Corresponding author for this work

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the 'filtering problem'; that is, to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy filter, based on the Cox process incorporating a shot noise process as claim intensity, we need to approximate it by a Gaussian process. We demonstrate that, if the primary-event arrival rate of the shot noise process is reasonably large, we can then approximate the intensity, claim arrival, and aggregate loss processes by a three-dimensional Gaussian process. We establish weak-convergence results. We then use the Kalman-Bucy filter and we obtain the price of reinsurance contracts involving high-frequency events.

Original languageEnglish
Pages (from-to)93-107
Number of pages15
JournalJournal of Applied Probability
Volume42
Issue number1
DOIs
Publication statusPublished - Mar 2005
Externally publishedYes

Keywords

  • Cox process
  • Gaussian process
  • Kalman-Bucy filter
  • Piecewise-deterministic Markov process theory
  • Shot noise process
  • Stop-loss reinsurance contract

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