Insurance and Actuarial Mathematics

Study of the disciplines of this educational program will develop mathematical apparatus that helps to model and solve tasks of actuarial mathematics. Actuary – is a specialist in charge of counting the damage and compensation for insurance and social companies.

After the end of the study the disciplines of the educational program "insurance and actuarial mathematics” students must:

Know and understand:

• technical specifications, designation, design features, rules of technical operation of local area network equipment, Office equipment, servers and personal computers;

• hardware and software, local area networks;

• repair of personal computers and office equipment

• programming methods and languages.

Be Able To:

• risk assessment, monitoring, analysis, calculation and adjustment of insurance rates;

• installed on server and Workstation operating systems and required to operate the software;

• identify and evaluate insurance reserves;

• monitor performance of loss of insurance products;

• configuration software on servers and workstations;

• maintain a healthy software servers and workstations;

Own:

• establishment of reinsurance premium technology and shares of reinsurer in insurance reserves;

• construction of structured cable systems technologies;

• Fundamentals of networking technology, CISCO;

• relevant technology cloud computing;

• technologies of preparation of statistical and analytical reports;

Catalogue of disciplines of the educational program

Catalogue of disciplines curriculum contains a description of each discipline separately with prerequisites and postrequisites, number of credits, activities, information on the management of the program.

Basic disciplines

Religion studies – 1 credit

Prerequisites - history of Kazakhstan.

Brief course content:

Religion as a subject and an object of religious studies course. The emergence of the religion. The structure and content of religion as a phenomenon. The specificity of the religious system of Ancient East and the Ancient world. Tengrianism, as early form of religious consciousness. Buddhism. Christianity, its origin and essence. The Holy book of the Christians. Main currents in Christianity. Islam. The Quran, the Sunnah, the Sharia. Main currents. Religious phenomenon in the modern world and Kazakhstan.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leaders: Shaimerden G.I., Bondarenko J.J.

Business etiquette – 1 credit

Prerequisites - history of Kazakhstan.

Brief course content: the History of development of etiquette. Peculiarities of business etiquette in different countries. Principles of etiquette of business relations. Formation of the image of a business person (clothing and appearance of a business man, a business woman). Business communication etiquette. Business communication, types, functions and levels. Rule of business etiquette. Ethics greetings, views. Business meeting. Presentation. Ethics of business telephone conversation. Business etiquette. Etiquette head. Etiquette Secretary. Everyday etiquette. Souvenirs and gifts in the business sphere. Code of honor of civil servants of the Republic of Kazakhstan (rules of ethics of civil servants). Code of ethics of students. Formation of corporate image. The modern Manager and its role in the formation of corporate image. Business rhetoric. Peculiarities of non-verbal means of communication. The basic precepts of business etiquette.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leader: Bayakhmetova A.A.

Psychology of competitive personality – 1 credit

Prerequisites - economic theory

Brief course content: the Personality. Constructive communication. A conflict. Technology of search of work. The basics of self-presentation. Development of the individual professional. Professional deformation, destruction of personality and ways of their prevention.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leader: Tashbaeva L.M.

Paperwork in the Kazakh language – 1 credit

Prerequisites - the Kazakh language.

Brief course content: Introduction. Name of official documents. Autobiography. Summary. A statement. Feature. A receipt. The power of attorney. Contract. The employment contract. Help. Resolution. Letters of congratulation. Official letters.

Postrequisites: the graduate's professional activity.

Types of classes: practical lessons.

Program leader: Kulbaeva M.M.

Programming – 2 credits

Prerequisites: Informatics

Brief course content: the Concept of algorithm, the program of the processed information. Technologies of development and implementation of algorithmic languages. The elements of the language. Alphabet, constants, identifiers, keywords, comments. Structured, modular programming. Basic concepts and mechanisms of entry environment and implementation of the programs. Basic data types. Basic principles of organization and structuring programs. Ads. Basic concepts and the language of the description of software objects. Operators. The main data processing tools. Pre-processing tools. Algorithmic foundations of writing efficient programs. The main principles and means of the organization of a software interface. Function. Main principles of development programs.

Postrequisites: discrete mathematics and mathematical logic

Types of classes: practical, laboratory classes

Program leader: Satmagambetova Zh.Z.

Object-based programming – 2 credits

Prerequisites: Informatics, programming

Brief course content: the Visual Basic language to create visual applications. Forms and controls. Declaration of variables, data types. Functions and procedures. The conditional operator, operator of multiple-choice cycles. Work with graphics. Management program progress. Debugging programs. Creating DLL libraries. Working with the file system. Implementation of data exchange between applications. Applications programming in MS Office.

Postrequisites: applied mathematics

Types of classes: practical, laboratory classes

Program leader: Ivanova I.V.

Мathematical analysis 3 – 3 credits

Prerequisites: mathematical analysis 1, mathematical analysis 2

Brief course content: the number series Main definitions. Properties of converging series. Number series with nonnegative members, signs of convergence. Alternating sequences, Signs alternating number series, a sign of Leibniz. Arithmetic on converging series. Functional sequences and series of Characteristics and properties of uniform convergence of functional sequences and series. Power series. Taylor Series. Weierstrass theorem on the uniform approximation of continuous functions by polynomials, trigonometric polynomials. Improper integrals I and type II. Properties. Absolute and conditional convergence of the improper integral. Integrals that depend on parameters of a Family of functions that his uniform convergence. The properties of limit functions. Own integrals that depend on a parameter; their properties, Leibniz formula. Improper integrals that depend on a parameter. Integrals Of Euler. G-function-function; their properties. Orthonormal systems and General Fourier series. The main theorem on convergence of trigonometric Fourier series. The principles of the Riemann localization. Some properties of the Fourier transform.

Postrequisites: differential equations, equations of mathematical physics

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Мathematical analysis 4 – 3 credits

Prerequisites: Мathematical analysis 1, mathematical analysis 2

Brief course content: Multiple integrals. Properties of integrals. Fold integral over an arbitrary set. Fubini theorem on reducing a multiple integral to the re. The change of variables in multiple integrals. Geometrical and physical applications of integrals. Curvilinear integrals in the I-St and II-nd kind. Properties curvilinear integrals in the I-St and II-nd kind. Green's Formula. Calculating the area of a flat area using the green's formula. Conditions of independence integral curved from the path of integration on the plane and space. The concept of the surface in three-dimensional space and ways to define a surface. The tangent plane and normal. Surface area. Surface integrals of the first and second kind. Conditions for the existence of surface integrals. Formula Ostrogradsky-Gauss, Stokes. Scalar and vector fields. Differential operators of vector analysis: the gradient of a scalar field, divergence and curl of a vector field. Their properties. The main integral formulas analysis in vector form. Solenoidal and potential fields.

Postrequisites: differential equations, equations of mathematical physics

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Мathematical stability theory – 3 credits

Prerequisites: mathematical analysis, differential equations

Brief course content: the Mathematical theory of stability. Basic concepts and theorems of the theory of stability. Stability of solutions of linear homogeneous systems of differential equations. The first method of investigation on stability. Direct method of investigation on stability. Stability in the first approximation. Stability of difference equations.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Introduction to Actuarial Mathematics – 3 credits

Prerequisites: a course of mathematical analysis, probability theory and mathematical statistics, financial mathematics.

Brief course content: the Main characteristics of life expectancy. Residual life time. Approximation for fractional ages. Life tables. Models of short-term life insurance. Models of long-term life insurance. The nature and the variety of reinsurance contracts. The actuarial present value and actuarial accumulation. Periodic prize. Calculation of protective overhead. Reserves. The main methods of reserves calculation. Yield insurance.

Postrequisites: actuarial mathematics, the theory of risk life insurance

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Equations of mathematical physics – 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra

Brief course content: Examples of physical problems leading to equations of mathematical physics. Setting of the Cauchy problem and boundary-value problems for the basic equations of mathematical physics. Notion solutions: classical and generalized. The correctness of the problem and the examples of ill-posed. Classification of equations and systems of equations with partial derivatives of the second order and bringing them to the canonical form. The concept of characteristics. Cauchy problem in a generalized setting. The Theorem Of Cauchy-Kovalevskaya. Cauchy problem for the wave equation and the wave propagation in unlimited space. The formulas of Duhamel, Poisson and Kirchhoff. Duhamel and its application for solving the Cauchy problem for these equations. The function of the Riemann problem for a hyperbolic equation with two independent variables and its properties. The task of the Cauchy and Goursat. A fundamental solution of the heat equation. Solution of the Cauchy problem for the heat equation. Formula For Poisson. The uniqueness of a solution of mixed problems. Thermal potentials, their properties and applications.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Dauletbaeva Zh.D.

Discrete mathematics and mathematical loqic – 3 credits

Prerequisites: elementary math, algebra

Brief course content: the set, elements of the set task sets. Set-based operations. Properties of the operations on sets. Combinatorics. Graph theory. The basic concepts and tasks of the theory of graphs. Charts-types, methods of setting the graphs. The coloring of graphs. Chromatic number. Euler on planar graphs. Estimates of the number of graphs. Logical operations on the statements. The formula. Complete systems of logical connectives. The formal system. Axioms and inference rule, YVES. Provability formulas. To derive formulas of the hypotheses. Models. Atomic predicate logic formulas, free and bound variables, quantifiers. Predicate logic formulas. Proven formula and formulas derived from a variety of hypotheses. Provability particular cases of tautology. Deduction theorem for calculation of predicates. Axiomatic building Peano arithmetic. Examples of formal conclusions of the laws of Peano arithmetic. Elements of the theory of algorithms. Turing Machine. The program of calculation of the simplest numerical functions. Composition of Turing machines. Encoding. Encoding. Encoding scheme. Alphabetic coding. Inequality Macmillan. Data compression. Compression texts. Dictionary. Algorithm of Lempel-Ziv. Encryption. Cryptography. Encryption by using random numbers. Public key cryptography.

Postrequisites: applied mathematics

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Theory of function analytic 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra.

Brief course content: the set of complex numbers. Algebraic form of a complex number. Functions of a complex variable. Continuity. Differentiability of functions of a complex variable. The integral of a function of a complex variable. Number series. Functional series. Power series. Theorem Abel. The radius of convergence. Laurent Series. Region of convergence of series of Laurent. Deduction of analytic functions in an isolated particular point. Conformal mapping.

Postrequisites: applied mathematics

Types of classes: practical lessons.

Program leader: Ysmagul R.S.

Matematical methods for calculathion of pension and other benefits – 3 credits

Prerequisites: probability theory and mathematical statistics

Brief course content: the actuarial control cycle. Providers of pensions and other benefits. Stakeholder satisfaction. Environment in which the benefit is also available. Schema design. Risks and uncertainties. Financing of benefits. Investment. An actuarial evaluation. Model evaluation assets. The assessment model of benefits. Methods of funding. Assumptions for the assessment. The termination. Data for the evaluation. Need assessment. Options and guarantees. Matching of assets and liabilities. Insurance. Sources of surplus. Analysis of the experience.

Postrequisites: actuarial mathematics and insurance of civil risks, risk theory

Types of classes: practical lessons.

Program leader: Ryshchanova S.M.

Algebraically systems – 3 credits

Prerequisites: elementary mathematics, basic algebra

Brief course content: Binary relations. Algebraic operations. The basic property relations: reflexivity, symmetry, transitivity, connectivity. Equivalence relation and auditing classes. Order relation. Factor set. Binary algebraic operations, examples. n-ary operations. Properties of binary relations in the two forms of recording. Algebraic systems. The Group Algebra. Algebraic systems. Semigroup. Subgroups. Theorem Of Lagrange. Normal divisors and the group factor. The kernel of the homomorphism. .Кольца. Ideals. Basic concepts. Examples of rings. Homomorphisms and isomorphisms of the rings, their properties. The kernel of the homomorphism. Zero divisors. The ratio of divisibility in a ring. The ratio of divisibility in the areas of integrity. Right and left ideals. Operations on the values .Главные ideals and their properties. Classes deductions module. Classes deductions ideal. Euclidean rings. Factor-ring. Field and body. Archimedean-closed fields. Numeric fields. Algebra Bull. Basic numeric system. The system of natural numbers. Axioms Of Peano. Method of complete mathematical induction. Arithmetic operations. Order relation. Ring of integers. The system of real numbers. Commutative rings with identity. Arithmetic operations and relations order. Ring of integers. The system of real numbers. Commutative rings with identity. Arithmetic operations and relations order. The ratio of divisibility in the ring of integers. Field of rational numbers. Ordered fields, thick ordering. Arithmetic operations. An equivalence relation. Quotient space.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Differential Geometry and Topology – 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra

Brief course content: the Theory of curves. Vector-valued functions. Definition of the curve in differential geometry. Ways of setting. Arc length and natural parameterization. The main theorem of the theory of curves. Theory of surfaces. The definition of the surface. Ways of setting. The curves on the surface. The first quadratic form. The second quadratic form of a surface. A surface of constant Gaussian curvature. Metric Euclidean space in curvilinear coordinates. Euclidean metric space (Minkowski space). A Riemannian metric on the surface. The metric of the Lobachevsky plane. A topological space. The topology of metric spaces. Continuous maps of topological spaces. Homeomorphism. Closed sets. Base topology. Compact topological space. Basic concepts of the theory of manifolds. Differentiable manifolds. Manifolds with edge. Oriented diversity. Functions on manifolds. Mapping of manifolds. Curves on a manifold. Vector fields on a manifold. Tensor fields on a manifold. Examples of tensor fields in mathematics and physics. Vector, quadratic forms, tensors of stress and strain and other Algebraic operations over tensor fields. A Riemannian metric on the manifold. External forms. The integration of differential forms on a smooth manifold. The General theorem Stokes equations. Special cases of a General formula for the Stokes equations.

Postrequisites: the actual analysis

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Actuarial Mathematics – 3 credits

Prerequisites: mathematical analysis

Brief course content: Basic survival function. Characteristics of survival. Qualifying tournaments and limit tables. The hypothesis of the laws of mortality. The main types of life insurance. Present value of the benefits. Variable pay. Recurrent formulas for non-recurring net premiums. Switching functions. Continuous payments. Differential equations for one-time net premiums. Lump-sum of net premium in case of multiples of payments. Annual annuities. The present value of an annuity. Continuous annuities. Differential equations for one-time net premiums. Lump-sum of net premium in case of multiples of payments. Annual annuities. The present value of an annuity. Continuous annuities. Differential equations for annuities. The cost of multiples of annuities. Contributions from returning. Contributions in the intermediate age groups. Regular net premium. Condition balance to regular premiums. Continuous net premium. Multiples of regular net premium. Prize with a condition of return.

Postrequisites: theory of risk, insurance of civil risks

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Profiling disciplines

Real Analysis – 3 credits

Prerequisites: mathematical analysis, basic algebra, analytical geometry.

Brief course content: the Topology of Euclidean spaces. Open and closed sets, their unions and intersections. The structure of open and closed sets on the line. Many everywhere dense and nowhere dense in the set. A measure of elementary sets. Lebegov’s measure of plane sets, its additive property. Proof of the closedness of the system of all measurable sets with regard to transactions taking finite or countable sums and intersections. The system sets. Ring and half ring sets. Ring, born of a semicircle, -algebra. The system sets and display the Definition of the measure on the belt sets. Continuation of measures with the semiring to emit them a ring. Lebegov’s continuation of the measures. Measurable functions. The definition and basic properties of measurable functions: measurability of the sum and product, private measurable functions. The convergence of sequences of functions almost everywhere and by measure. Measurable limit almost everywhere of measurable functions. The theorem about the relationship between various types of convergence. Simple functions. Lebesgue integral for simple functions and properties. A General definition of the integrals of Lebesgue measure on the set of final measures. -additivity and the absolute continuity of the Lebesgue integral. The passage to the limit under the integral sign Lebesgue measure. The Theorems Of Lebesgue, Levi, A Veil. Comparison of the Lebesgue integral with the Riemann integral. Works of systems of sets. Works of measures. Fubini Theorem. Monotone functions. Differentiability of integrals on the upper limit. Functions with a limited change. The restoration of the function on its derivative. Absolutely continuous functions. The charges. Absolutely continuous charges. Theorem, Radon-Nikodim. Measures Lebesgue-Stieltjes Transform. Integral Lebesgue-Stieltjes and integral Riemann-Stieltjes

Postrequisites: applied mathematics.

Types of classes: practical lessons.

Program leader: Kalzhanov M.U.

The differential equations in private derivatives – 3 credits

Prerequisites: mathematical analysis, differential equations, equations of mathematical physics

Brief course content: the Equations with partial derivatives of the first order from one unknown function. Квазилинейные equations. Nonlinear equations. Integral surface for the equation of Pfaff. Classification of quasi-linear differential equations of the second order. The expression of the Laplace operator in spherical and cylindrical coordinates. The canonical form of the equations with two independent variables. Tasks leading to the study of solutions of the Laplace equation. Potential stationary electrical current. Linear integral equations. Basic concepts. Classification of integral equations.

Postrequisites: applied mathematics.

Types of classes: practical lessons.

Program leader: Ysmagul R.S.

Applied Mathematics – 3 credits

Prerequisites: mathematical analysis, actuarial mathematics

Brief course content: Numerical methods. The theory of games. Operations research. Linear programming. Graph theory. The theory of insurance. Thorium information.

Postrequisites: management of investments, assets, mathematical models of insurance

Types of classes: practical lessons.

Program leader: Ryshchanova S.M.

Insurance risk civil -2 credits

Prerequisites: actuarial mathematics, mathematical methods of calculation of pension and other benefits.

Brief course content: the Concept of risk. The concept of uncertainty. The concept of damage. Factors increasing the risk level. Possible consequences of risk. Classification of risks: the insured and not insurable, pure and speculative, static and dynamic risks, permanent and temporary, business, currency, innovative, etc. Stages of risk management. The preparatory phase. The implementation stage.: defining the objective elucidation of risk, risk assessment. Methods of risk assessment. The concept of the middle group. The method of individual assessment. Method of averages. Method percent. Ways to minimize risks elimination, loss prevention and control, insurance, absorption.

Postrequisites: mathematical models of insurance.

Types of classes: practical, laboratory

Program leader: Kalzhanov M.U.

Investment and asset management – 2 credits

Prerequisites: mathematical analysis, probability theory and mathematical statistics, introduction to actuarial mathematics

Brief course content: the actuarial control cycle in General insurance. Taxation. Assessment of investment program. Money markets. The bond or stock markets. Derivative instruments. Investment in real estate. Media joint investments. Foreign investments. Fundamental analysis of the shares. Factors influencing the relative assessment. Investment indices and assessment of individual investments. The relationship between the return on the different asset classes. Evaluation classes of assets and portfolios. Definition of quality of work. Portfolio management and strategy development. Framework for organizations. Regulation of financial services. Personal investment.

Postrequisites: mathematical models of insurance

Types of classes: practical lessons.

Program leader: Kalzhanov M.U.

Mathematical models of insurance – 3 credits

Prerequisites: introduction to actuarial mathematics, actuarial mathematics, management of investments and assets

Brief course content: the Model of the Cramer-Lundberg. Assessment of risk of ruin of an insurance company, determination of the size of the insurance premium. Statistical methods of calculating the average size of insurance payments. Calculation of the probability of occurrence. Revenues, expenses and profit insurance. Insured risks and insurance protection. Materialization of insurance protection. Reinsurance in insurance market

Postrequisites: risk theory.

Types of classes: practical lessons.

Program leader: Ryshchanova S.M.

Risk theory – 3 credits

Prerequisites: probability theory and mathematical statistics, introduction to actuarial mathematics

Brief course content: the Distribution of damage. The calculation of premiums. Net and gross premiums. Reinsurance. Proportional and non-proportional reinsurance. Theory of ruin. Own funds, Poisson and generalized Poisson processes, the correction factor and inequality Lundberg. Probability of ruin. Bayesian techniques. Bayes' formula, function damage and Bayesian estimation. The plausibility theory. Bayesian approach to decision making. Empirical Bayesian model. Time series. Additive time series, autocorrelation, autoregression. Types of reserves. Triangles development. The basic method chain ladder. Inflation accounting. Discounts for stop-loss insurance.

Postrequisites:no

Types of classes: practical lessons.

Program leader: Dauletbaeva Zh.D.