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Scenario Analysis for a Multi-Period Diffusion Model of Risk

Published online by Cambridge University Press:  09 August 2013

Vsevolod K. Malinovskii
Vsevolod K. Malinovskii*
Affiliation:
Finance Academy, 125468, Leningradskiy prosp., 49, Moscow, Russia, and Steklov Mathematical Institute, 119991, Gubkina Str., 8, Moscow, Russia, E-mail: malinov@orc.ru, malinov@mi.ras.ru, URL: http://www.actlab.ru
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Abstract

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This paper extends and develops the results of a previous paper Malinovskii (2007). Dealing with a simplistic diffusion multi-year model of insurance operations, this paper illustrates the adaptive control approach when the object of control is the balance of solvency and equity. Compared to the previous paper, a new element is the “scenario of nature”, or the incomplete knowledge of future risk, which is quite often the case in insurance. It introduces a new and inevitable randomness in the model and leads to a qualitative difference in its behavior.

Keywords

Multi-period insurance processDiffusion annual mechanismsVolatile scenarioSolvencyEquityAdaptive control strategies
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 649 - 676
Copyright
Copyright © International Actuarial Association 2009

References

Asmussen, S. and Taksar, M. (1997) Controlled diffusion models for optimal dividend payout. Insurance: Mathematics and Economics 20, 1–15.Google Scholar
Borch, K. (1967) The theory of risk. Journal of the Royal Statist. Soc., Ser B 29, no. 3, 432–452 Google Scholar
Borch, K. (1967) The theory of risk. Journal of the Royal Statist. Soc., Ser B 29, no. 3 Discussion, 452–467.Google Scholar
Borodin, A.N. and Salminen, P. (1996) Handbook of Brownian Motion. Facts and Formulæ. Birkhäuser, Basel.CrossRefGoogle Scholar
Dacorogna, M. and Rüttener, E. (2006) Why time-diversi?ed equalization reserves are something worth having. Insurance Day, February 2006.Google Scholar
Daykin, C.D., Pentikäinen, T. and Pesonen, M. (1996) Practical Risk Theory for Actuaries. Chapman and Hall, London, etc.Google Scholar
Gihman, I.I. and Skorokhod, A.V. (1979) Controlled Stochastic Processes. Springer-Verlag, New York etc.CrossRefGoogle Scholar
Malinovskii, V.K. (2007) Zone-adaptive control strategy for a multiperiodic model of risk. Annals of Actuarial Science 2, II, 349–367.Google Scholar
Malinovskii, V.K. (2008a) Adaptive control strategies and dependence of finite time ruin on the premium loading. Insurance: Mathematics and Economics 42, 81–94.Google Scholar
Malinovskii, V.K. (2008b) Risk theory insight into a zone-adaptive control strategy. Insurance: Mathematics and Economics 42, 656–667.Google Scholar
Patel, J.K. and Read, C.R. (1982) Handbook of the Normal Distributions. Marcel Dekker.Google Scholar
Taksar, M. and Zhou, X.Y. (1998) Optimal risk and dividend control for a company with a debt liability. Insurance: Mathematics and Economics 22, 105–122.Google Scholar
Wiener, N. (1966) God and Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion, The M.I.T. Press.Google Scholar