A Cox model for gradually disappearing events

Jiwook Jang, Yan Qu, Hongbiao Zhao and Angelos Dassios

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Innovations in medicine provide us longer and healthier life, leading lower mortality. Sooner rather than later, much greater longevity would be possible for us due to artificial intelligence advances in health care. Similarly, Advanced Driver Assistance Systems (ADAS) in highly automated vehicles may reduce or even eventually eliminate accidents by perceiving dangerous situations, which would minimize the number of accidents and lead to fewer loss claims for insurance companies. To model the survivor function capturing greater longevity as well as the number of claims reflecting less accidents in the long run, in this paper, we study a Cox process whose intensity process is piecewise-constant and decreasing. We derive its ultimate distributional properties, such as the Laplace transform of intensity integral process, the probability generating function of point process, their associated moments and cumulants, and the probability of no more claims for a given time point. In general, this simple model may be applicable in many other areas for modeling the evolution of gradually disappearing events, such as corporate defaults, dividend payments, trade arrivals, employment of a certain job type (e.g., typists) in the labor market, and release of particles. In particular, we discuss some potential applications to insurance.

Keywords: Point process; Cox process; Cox process with piecewise-constant decreasing intensity; gradually disappearing events; survival probability; competing risks; stop-loss reinsurance (search for similar items in EconPapers)
JEL-codes: J01 R14 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2023-01-01
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Published in Probability in the Engineering and Informational Sciences, 1, January, 2023, 37(1), pp. 214 - 231. ISSN: 0269-9648

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