Robust LMI stability of a premium pricing model into a discrete-time stochastic framework

Athanasios A. Pantelous; Lin Yang

doi:10.1061/9780784413609.107

Robust LMI stability of a premium pricing model into a discrete-time stochastic framework

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

The premium pricing process and the stability of the reserves are two very challenging issues in the insurance industry. In practice, a premium which is sufficient enough to cover the expected claims and to stabilize the derived reserves is always required. This paper proposes a premium pricing model for general insurance products which implements a negative feedback mechanism for the known reserves with time-varying, bounded delays and is based on the recent claim experience into a stochastic framework with norm-bounded parameter uncertainties. The robust stability for the reserve process is investigated using Linear Matrix Inequality (LMI) criteria in a discrete-time stochastic framework. A numerical example illustrates the main result of the paper.

Original language	English
Title of host publication	Vulnerability, Uncertainty, and Risk
Subtitle of host publication	Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA)
Editors	Michael Beer, Siu-Kui Au, Jim W. Hall
Place of Publication	Reston VA USA
Publisher	American Society of Civil Engineers
Pages	1057-1066
Number of pages	10
ISBN (Electronic)	9780784413609
DOIs	https://doi.org/10.1061/9780784413609.107
Publication status	Published - 2014
Externally published	Yes
Event	International Conference on Vulnerability and Risk Analysis and Management and the International Symposium on Uncertainty Modeling and Analysis 2014 - University of Liverpool, Liverpool, United Kingdom Duration: 13 Jul 2014 → 16 Jul 2014 http://www.icvram2014.org/

Conference

Conference	International Conference on Vulnerability and Risk Analysis and Management and the International Symposium on Uncertainty Modeling and Analysis 2014
Abbreviated title	ASCE-ICVRAM-ISUMA 2014
Country/Territory	United Kingdom
City	Liverpool
Period	13/07/14 → 16/07/14
Other	2nd International Conference on Vulnerability and Risk Analysis and Management and the 6th International Symposium on Uncertainty Modeling and Analysis
Internet address	http://www.icvram2014.org/

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10.1061/9780784413609.107

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Pantelous, A. A., & Yang, L. (2014). Robust LMI stability of a premium pricing model into a discrete-time stochastic framework. In M. Beer, S.-K. Au, & J. W. Hall (Eds.), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA) (pp. 1057-1066). American Society of Civil Engineers. https://doi.org/10.1061/9780784413609.107

Pantelous, Athanasios A. ; Yang, Lin. / Robust LMI stability of a premium pricing model into a discrete-time stochastic framework. Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). editor / Michael Beer ; Siu-Kui Au ; Jim W. Hall. Reston VA USA : American Society of Civil Engineers, 2014. pp. 1057-1066

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abstract = "The premium pricing process and the stability of the reserves are two very challenging issues in the insurance industry. In practice, a premium which is sufficient enough to cover the expected claims and to stabilize the derived reserves is always required. This paper proposes a premium pricing model for general insurance products which implements a negative feedback mechanism for the known reserves with time-varying, bounded delays and is based on the recent claim experience into a stochastic framework with norm-bounded parameter uncertainties. The robust stability for the reserve process is investigated using Linear Matrix Inequality (LMI) criteria in a discrete-time stochastic framework. A numerical example illustrates the main result of the paper.",

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publisher = "American Society of Civil Engineers",

address = "United States of America",

note = "International Conference on Vulnerability and Risk Analysis and Management and the International Symposium on Uncertainty Modeling and Analysis 2014, ASCE-ICVRAM-ISUMA 2014 ; Conference date: 13-07-2014 Through 16-07-2014",

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Pantelous, AA & Yang, L 2014, Robust LMI stability of a premium pricing model into a discrete-time stochastic framework. in M Beer, S-K Au & JW Hall (eds), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). American Society of Civil Engineers, Reston VA USA, pp. 1057-1066, International Conference on Vulnerability and Risk Analysis and Management and the International Symposium on Uncertainty Modeling and Analysis 2014, Liverpool, United Kingdom, 13/07/14. https://doi.org/10.1061/9780784413609.107

Robust LMI stability of a premium pricing model into a discrete-time stochastic framework. / Pantelous, Athanasios A.; Yang, Lin.
Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). ed. / Michael Beer; Siu-Kui Au; Jim W. Hall. Reston VA USA: American Society of Civil Engineers, 2014. p. 1057-1066.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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PY - 2014

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AB - The premium pricing process and the stability of the reserves are two very challenging issues in the insurance industry. In practice, a premium which is sufficient enough to cover the expected claims and to stabilize the derived reserves is always required. This paper proposes a premium pricing model for general insurance products which implements a negative feedback mechanism for the known reserves with time-varying, bounded delays and is based on the recent claim experience into a stochastic framework with norm-bounded parameter uncertainties. The robust stability for the reserve process is investigated using Linear Matrix Inequality (LMI) criteria in a discrete-time stochastic framework. A numerical example illustrates the main result of the paper.

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Pantelous AA, Yang L. Robust LMI stability of a premium pricing model into a discrete-time stochastic framework. In Beer M, Au SK, Hall JW, editors, Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). Reston VA USA: American Society of Civil Engineers. 2014. p. 1057-1066 doi: 10.1061/9780784413609.107

Robust LMI stability of a premium pricing model into a discrete-time stochastic framework

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