Advances in Intelligent Systems and Computing 441
George A. Anastassiou Oktay Duman Editors
Mathematics II:
Applied Mathematics
and Approximation
Theory
Contents
Bivariate Left Fractional Polynomial Monotone Approximation . . . 1 George A. Anastassiou
Bivariate Right Fractional Pseudo-Polynomial Monotone
A p p roxim ation ... 15 George A. Anastassiou
Nonlinear Approximation: q-Bernstein Operators of M ax-Product
K i n d ... 33 Oktay Duman
A Two Dim ensional Inverse Scattering Problem for Shape
and Conductive Function for a Dielectic C ylinder... 57 Ahmet Altundag
Spinning Particle in Interaction with a Time Dependent M agnetic
Field: A Path Integral A p p ro a ch ... 73 Hilal Benkhelil and Mekki Aouachria
New Complexity Analysis of the Path Following Method
for Linear Complementarity P r o b le m ... 87 El Amir Djeffal, Lakhdar Djeffal and Farouk Benoumelaz
Branch and Bound Method to Resolve the Non-convex
Quadratic P r o b le m s ... 105 R. Benacer and Boutheina Gasmi
Rogue W ave Solutions for the Myrzakulov-I E q u a tio n ... 119 Gulgassyl Nugmanova
Fuzzy Bilevel Programming with Credibility M easure... 127 Hande Giinay Akdemir
A New Approach o f a Possibility Function Based Neural Network . . . . 139 George A. Anastassiou and Iuliana F. Iatan
ix
x Contents
Elem entary M atrix Decomposition Algorithm for Symmetric Extension o f Laurent Polynomial Matrices and Its Application
in Construction o f Symmetric М -Band Filter B a n k s... 151 Jianzhong W ang
Solution o f Equation for Ruin Probability of Company for Some
Risk M odel by M onte Carlo M e t h o d s ... 169 Kanat Shakenov
Determinant Reprentation of Dardoux Transformation
for the (2+l)-D im ensional Schrodinger-Maxwell-Bloch E q u a tio n ... 183 K.R. Yesmahanova, G.N. Shaikhova, G.T. Bekova
and Zh.R. M yrzakulova
Numerical Solution of Nonlinear Klein-Gordon Equation
Using Polynom ial Wavelets . ... ... 199 Jalil Rashidinia and M ahmood Jokar
A New Approach in Determining Lot Size in Supply Chain
Using Game T h e o r y ... 215 M aryam Esmaeili
Voronovskaya Type Asymptotic Expansions for Multivariate
Generalized Discrete Singular O p era to rs... 233 George A. Anastassiou and Merve Kester
Variational Analysis of a Quasistatic Contact P r o b le m ... 245 M ircea Sofonea
Efficient Lower Bounds for Packing Problems in Heterogeneous
Bins with Conflicts C onstraint... 263 M ohamed Maiza, M ohammed Said Radjef and Lakhdar Sais
Global Existence, Uniqueness and Asymptotic Behavior
for a Nonlinear Parabolic S y s t e m ... 271 Naima A'fssa and H. Tsamda
M athematical Analysis of a Continuous Crystallization P rocess... 283 Amira Rachah and Dominikus Noll
W ave Velocity Estimation in Heterogeneous M edia... 303 Sharefa Asiri and Taous-Meriem Laleg-Kirati
Asymptotic Rate for Weak Convergence of the Distribution
o f Renewal-Reward Process with a Generalized Reflecting Barrier . . . . 313 Tahir Khaniyev, Ba§ak Gever and Zulfiye Hanalioglu
312 S. Asiri and T.-M. Laleg-Kirati
References
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Solution of Equation for Ruin Probability of Company for Some Risk Model
by Monte Carlo Methods
Kanat Shakenov
A bstract The classical process o f risk and the equation for ruin probability o f some model (model S. Anderson) is considered. This model is solved by classical numerical methods and M onte Carlo methods.
1 Introduction
Risk. We are interested not so much in the outcome o f a process as the associated quantitative characteristics. The risk can be described by a random variable. The meaning o f the word “risk” is probabilistic in nature, therefore, we shall call the risk as arbitrary random variable. The set of all risks is denoted X (see [6-10]).
The risk portfolio. The risk portfolio P is said to be an arbitrary subset of X.
Insurance. Insurance is a transfer o f risk from one carrier (the insured) to another (the insurance company, the insurer) for a fee, called the cost of insurance, tariff rates or premiums. The essence of insurance is to redistribute risk among multiple carriers; relatively homogeneous set of risks will be called insurance portfolio.
Insurance portfolio. The simplest insurance portfolio. The simplest insurance portfolio
P = { X , , . . . , X W) consists of N risks (random variables)
X U . . . , X N,
K. Shakenov (E3)
A l-F arab i K aza k h N atio n al U n iv ersity , A lm aty , K aza k h stan e -m ail: sh a k e n o v 2 0 0 0 @ m a il.ru
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