0
Research Papers

Robust H-Infinity Control for a Premium Pricing Model With a Predefined Portfolio Strategy

[+] Author and Article Information
Athanasios A. Pantelous

Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics (IFAM);Institute for Risk and Uncertainty, University of Liverpool, Peach Street, Liverpool L697ZL, UKe-mail: A.Pantelous@liverpool.ac.uk

Lin Yang

Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics (IFAM), University of Liverpool, Peach Street, Liverpool L697ZL, UK

1Corresponding author.

Manuscript received September 19, 2014; final manuscript received February 3, 2015; published online April 20, 2015. Assoc. Editor: James Lambert.

ASME J. Risk Uncertainty Part B 1(2), 021006 (Apr 20, 2015) (8 pages) Paper No: RISK-14-1057; doi: 10.1115/1.4029758 History: Received September 19, 2014; Accepted February 05, 2015; Online April 20, 2015

In this paper, the robust H-infinity (H) control problem for a premium pricing process is investigated with parameters uncertainty. A previous model is modified by taking into account a predefined risky investment strategy. A robust H control problem for the reserve process is proposed using linear matrix inequality (LMI) criteria. Attention is focused on the design of a state feedback controller such that the resulting closed-loop system is robustly stochastically stable with disturbance attenuation level γ>0. Finally, a numerical example with colorful figures and tables based on the data from the Shanghai Stock Exchange market is provided illustrating clearly the impact of risky investment in the system. The MATLAB LMI Control toolbox is used for the numerical calculations.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

De Finetti, B., 1957, “Su una Impostazione Alternativa Della Theoria Collectiva del Rischio,” Transactions of the 15th International Congress of Actuaries, New York, Vol. II, pp. 433–443.
Borch, K., 1967, “The Theory of Risk,” J. R. Stat. Soc. (Ser. B), 29(3), pp. 432–452.
Balzer, L. A., and Benjamin, S., 1980, “Dynamic Response of Insurance Systems With Delayed Profit/Loss Sharing Feedback to Isolated Unpredicted Claims,” J. Inst. Actuaries, 107(4), pp. 513–528. 10.1017/S0020268100040464
Balzer, L. A., 1982, “Control of Insurance Systems With Delayed Profit/Loss Sharing Feedback and Persisting Unpredicted Claims,” J. Inst. Actuaries, 109(2), pp. 285–316. 10.1017/S0020268100036271
Martin-Löf, A., 1983, “Premium Control in an Insurance System, an Approach Using Linear Control Theory,” Scand. Actuarial J., 1983(1), pp. 1–27. 10.1080/03461238.1983.10408686
Zimbidis, A. A., and Haberman, S., 2001, “The Combined Effect of Delay and Feedback on the Insurance Pricing Process: A Control Theory Approach,” Insur. Math. Econ., 28(2), pp. 263–280.
Pantelous, A. A., and Yang, L., 2014, “Robust LMI Stability, Stabilization and Hoo Control for Premium Pricing Models With Uncertainties Into a Stochastic Discrete-Time Framework,” Insur. Math. Econ., 59, pp. 133–143. [CrossRef]
Pantelous, A. A., and Papageorgiou, A., 2013, “On the Robust Stability of Pricing Models for Non-Life Insurance Products,” Eur. Actuarial J., 3(2), pp. 535–550. 10.1007/s13385-013-0074-8
Xu, S., Lam, J., and Chen, T., 2004, “Robust H∞ Control for Uncertain Discrete Stochastic Time-Delay Systems,” Sys. Control Lett., 51(3–4), pp. 203–215. 10.1016/j.sysconle.2003.08.004
Wang, Y., Xie, L., and de Souza, C. E., 1992, “Robust Control of a Class of Uncertain Nonlinear Systems,” Sys. Control Lett., 19(2), pp. 139–149. 10.1016/0167-6911(92)90097-C

Figures

Grahic Jump Location
Fig. 1

Premium for the three products for the case 6: (m1=50%, m2=50%)

Grahic Jump Location
Fig. 2

Accumulated reserve for the three products for the case 6: (m1=50%, m2=50%)

Grahic Jump Location
Fig. 3

Premium for product 2 for the case 1: (m1=100%, m2=0%), 6: (m1=50%, m2=50%) and 11: (m1=0%, m2=100%)

Grahic Jump Location
Fig. 4

Accumulated reserve for product 2 for the case 1: (m1=100%, m2=0%), 6: (m1=50%, m2=50%) and 11: (m1=0%, m2=100%)

Grahic Jump Location
Fig. 5

Total premium for the case 1: (m1=100%, m2=0%), 6: (m1=50%, m2=50%) and 11: (m1=0%, m2=100%)

Grahic Jump Location
Fig. 6

Total reserve for the case 1: (m1=100%, m2=0%), 6: (m1=50%, m2=50%) and 11: (m1=0%, m2=100%)

Grahic Jump Location
Fig. 7

Disturbance level wn for product 2 for all cases: from t=0 to t=52

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Articles from Part A: Civil Engineering
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In