A Cox Model for Gradually Disappearing Events

Probability in the Engineering and Informational Sciences, 37(1), 214-231, 2023​

23 Pages Posted: 9 Jun 2022 Last revised: 27 Jul 2023

See all articles by Jiwook Jang

Jiwook Jang

Macquarie University; Financial Research Network (FIRN); Macquarie University, Macquarie Business School

Yan Qu

University of Warwick - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Date Written: December 6, 2021

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 minimise 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 modelling 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

JEL Classification: 91B30

Suggested Citation

Jang, Jiwook and Qu, Yan and Zhao, Hongbiao and Dassios, Angelos, A Cox Model for Gradually Disappearing Events (December 6, 2021). Probability in the Engineering and Informational Sciences, 37(1), 214-231, 2023​, Available at SSRN: https://ssrn.com/abstract=4122209 or http://dx.doi.org/10.2139/ssrn.4122209

Jiwook Jang

Macquarie University ( email )

Actuarial Studies
Faculty of Business and Economics
Sydney NSW 2109
Australia
+61 2 9850 8575 (Phone)
+61 2 9850 9481 (Fax)

HOME PAGE: http://be.mq.edu.au/contact_the_faculty/staff/alphabetical_list_of_staff/Jiwook_Jang

Financial Research Network (FIRN) ( email )

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Yan Qu

University of Warwick - Department of Statistics ( email )

Coventry, CV47AL
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

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