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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

## Abstract

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.

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## Figures

Fig. 1

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

Fig. 2

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

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%)

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%)

Fig. 5

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

Fig. 6

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

Fig. 7

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

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