Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-30T09:10:39.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Zone-Adaptive Control Strategy for a Multiperiodic Model of Risk

Published online by Cambridge University Press:  10 May 2011

V. K. Malinovskii
V. K. Malinovskii
Affiliation:
Finance Academy, 125468, Leningradskiy prosp., 49, Moscow, Russia, and Steklov Mathematical Institute, 119991, Gubkina Str., 8, Moscow, Russia
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is intended to illustrate the adaptive control approach in insurance. A zone-adaptive control strategy harmonising the requirements of principles of solvency and equity is considered in the simplistic framework of a diffusion multiperiodic risk model. Other works by the author set similar adaptive control strategies in a more realistic Poisson-exponential multiperiodic risk model. There is much scope for further generalisations.

Keywords

Multiperiodic Insurance ProcessEquitySolvencyZone-Adaptive ControlDiffusion Risk Model
Type
Papers
Information
Annals of Actuarial Science , Volume 2 , Issue 2 , September 2007 , pp. 349 - 367
Copyright
Copyright © Institute and Faculty of Actuaries 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Asmussen, S. (1984). Approximations for the probability of ruin within finite time. Scandinavian ActuarialJournal, 64, 31–57.CrossRefGoogle Scholar
Asmussen, S & Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics, 20, 1–15.Google Scholar
Borch, K. (1967). The theory of risk. Journal of the Royal Statistical Society, Series B, 29(3), 432–452; discussion,Google Scholar
Borch, K. (1967). The theory of risk. Journal of the Royal Statistical Society, Series B, 29(3), 452–467.Google Scholar
Borodin, A.N. & Salminen, P. (1996). Handbook of Brownian motion. Facts and formulae. Birkhäuser, Basel.CrossRefGoogle Scholar
Bühlmann, H. (1970). Mathematical methods in risk theory. Springer-Verlag, New York.Google Scholar
Daykin, C.D., Pentikäinen, T. & Pesonen, M. (1996). Practical risk theory for actuaries. Chapman and Hall, London, etc.Google Scholar
Directive 2002 /13/ EC of the European Parliament and of the Council of 5 March 2002 (2002). Brussels, 5 March 2002.Google Scholar
Garrido, J. (1986). Weak convergence of risk processes, In (Goovaerts, M.et al., eds.) Insurance and risk theory. D. Reidel Publishing Company, 349–360.Google Scholar
Gihman, I.I. & Skorokhod, A.V. (1979). Controlled stochastic processes. Springer-Verlag, New York, etc.Google Scholar
Grandell, J. (1977). A class of approximations of ruin probabilities. Scandinavian Actuarial Journal, Suppl., 37–52.CrossRefGoogle Scholar
Harrison, M. (1977). Ruin problems with compounding assets. J. Stoch. Proc. Appl, 5, 67–79.CrossRefGoogle Scholar
Iglehart, D.L. (1969). Diffusion approximations in collective risk theory. Journal of Applied Probability, 6, 285–292.CrossRefGoogle Scholar
Lerche, H.R. (1986). Boundary crossing of Brownian motion. Lecture Notes in Statistics, 40, Springer, Berlin.Google Scholar
Malinovskii, V.K. (2003). On a non-linear dynamic solvency control model. Contribution to: XXXIV ASTIN Colloquium, Berlin, 24–27 August.Google Scholar
Malinovskii, V.K. (2006). Risk theory insight into the asset-liability and solvency adaptive management. Contribution to 28th International Congress of Actuaries, Paris, May.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
Ruohonen, M. (1980). On the probability of ruin of risk processes approximated by a diffusion process. Scandinavian Actuarial Journal, 113–120.CrossRefGoogle Scholar
Siegmund, D. (1979). Corrected diffusion approximation in certain random walk problems. Advances in Applied Probability, 11, 701–719.Google Scholar
Solvency Control Levels, Draft Guidance Paper. IAIS Subcommittee on Solvency and Actuarial Issues, Draft version 24 June 2002.Google Scholar
Taksar, M. & 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