AUTHORS: S. Khotama, S. Boonthiem, W. Klongdee
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ABSTRACT: The adaptive moving total least square (AMTLS) method has been used for curve fitting. In this study, AMTLS method is used for the ruin probability fitting and estimation of the ruin probability on an arbitrary initial capital in finite-time surplus process (or risk process). But in reality, it is difficult and complicated to find a fitting method for an appropriate estimate in order to obtain the best performance. So, a new method is developed to estimate the ruin probability of finite-time surplus process. This new method is called adaptive moving total exponential least square (AMTELS) method that applies AMTLS method with least-square fitting exponential. Claim data of motor insurance company from Thailand has used in risk process for the ruin probability fitting. Both AMTLS and AMTELS methods consider weighted function for the distance between node and point with a different constant value d. These methods are compared the performance by using the mean squared error (MSE) and the mean absolute error (MAE) that is, the error between the real ruin probability value that is obtained by the explicit formula and the ruin probability fitting value. With these data, the ruin probability approximating examples are given to prove that AMTELS method shows the better performance than AMTLS method. Moreover, AMTELS method with the narrow value d shows the better performance than AMTELS method with the wide value d.
KEYWORDS: - Adaptive moving total least square, exponential claim, least-square fitting exponential, moving total least squares, the ruin probability fitting, weighted function
REFERENCES:
[1] J. Grandell, Aspects of Risk Theory, New York:
Springer-Verlag, 1990.
[2] W. S. Chan and L. Zhang, Direct derivation of
finite-time ruin probabilities in the discrete risk
model with exponential or geometric claims,
North American Actuarial Journal, Vol.10,
No.4, 2006, pp. 269-279.
[3] P. Sattayatham, K. Sangaroon, and W.
Klongdee, Ruin Probability-Based Initial
Capital of the Discrete-Time Surplus Process,
Variance, Vol.7, No.1, 2013, pp. 74-81.
[4] S. Khotama, K. Sangaroon, and W. Klongdee,
A sufficient condition for reducing the finitetime
ruin probability under proportional
reinsurance in discrete-time surplus process,
Far East Journal of Mathematical Sciences
(FJMS), Vol.96, No.5, 2015, pp. 641-650.
[5] H. Jasiulewicz and W. Kordecki, Ruin
probability of a discrete-time risk process with
proportional reinsurance and investment for
exponential and Pareto distributions,
Operations Research and Decisions, Vol.25,
No.3, 2015, pp. 17-38.
[6] S. Khotama, T. Thongjunthug, K. Sangaroon,
and W. Klongdee, On Approximating the
Minimum Initial Capital of Fire Insurance with
the Finite-time Ruin Probability using a
Simulation Approach, Asia-Pacific Journal of
Science and Technology (APST), Vol.20, No.3,
2015, pp. 267-271.
[7] W. Klongdee and S. Khotama, Minimizing the
Initial Capital for the Discrete-time Surplus
Process with Investment Control under Alpharegulation
(Published Conference Proceedings
style), in the International MultiConference of
Engineers and Computer Scientists 2018, Hong
Kong, 2018, pp. 299-301.
[8] R. Scitovski, S. Ungar, D. Juki ́, and M.
Crnjac, Moving Total Least Squares for
Parameter Identification in Mathematical
Model, Operations Research Proceedings,
Springer, Berlin, Vol. 1995, pp. 196-201.
[9] R. Scitovski, ̌. Ungar, and D. Juki ́,
Approximating surfaces by moving total least
squares method, Applied Mathematics and
Computation, Vol. 93, No.1-2, 1998, pp. 219-
232.
[10] Z. Lei, G. Tianqi, Z. Ji, J. Shijun, S.
Qingzhou, and H. Ming, An adaptive moving
total least squares method for curve fitting,
Measurement, Vol. 49, 2014, pp. 107-112.
[11] U. H. Combe and C. Korn, An adaptive
approach with the Element-Free-Galerkin
method, Computer methods in applied
mechanics and engineering, Vol.162, No.1-4,
1998, pp. 203-222
WSEAS Transactions on Business and Economics, ISSN / E-ISSN: 1109-9526 / 2224-2899, Volume 15, 2018, Art. #31, pp. 321-328
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