INSTITUTE OF APPLIED MATHEMATICS
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28/08/2017 - 21:10

All Courses @ IAM Actuarial Science Cryptography Financial Mathematics Scientific Computing

Selected Courses for Actuarial Science

Credit: 0(0-0); ECTS: 50.0

The Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters while the research program or write up of thesis is in progress. Student must start registering to this course no later than the second semester of his/her M.S. study.

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Credit: 3(3-0); ECTS: 8.0

Examination of special issues in finance incorporating advanced theory and practice with emphasis on investment and financing decisions of the firm. Special references to applications in Turkey. Outline of Topics: An Overview of Financial Management. Financial Statements, Cash Flow, and Taxes. Analysis of Financial Statements. The Financial Environment: Markets, Institutions, and Interest Rates. Risk and Return. Time Value of Money. Bonds and Their Valuation. Stocks and Their Valuation. The Cost of Capital. The Basics of Capital Budgeting. Cash Flow Estimation and Other Topics in Capital Budgeting. Capital Structure Decisions. Distribution to Shareholders: Dividends and Repurchases. Issuing Securities, Refunding, and Other Topics. Lease Financing. Current Asset Management. Mergers, LBOs, Divestitures, and Holding Companies.

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Credit: 3(3-0); ECTS: 8.0

The objective of this course is an introduction to the probabilistic techniques required for understanding the most widely used financial models. In the last few decades, financial quantitative analysts have used sophisticated mathematical concepts in order to describe the behavior of markets and derive computing methods. The course presents the martingales, the Brownian motion, the rules of stochastic calculus and the stochastic differential equations with their applications to finance. Outline of Topics: Discrete time models, Martingales and arbitrage opportunities, complete markets, European options, option pricing, stopping times, the Snell envelope, American options. Continuous time models: Brownian motion, stochastic integral with respect to the Brownian motion, the Itô Calculus, stochastic differential equations, change of probability, representation of martingales; pricing and hedging in the Black-Scholes model, American options in the Black-Scholes model; option pricing and partial differential equations; interest rate models; asset models with jumps.

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Credit: 3(3-0); ECTS: 8.0

Part I: Probability spaces, random variables, probability distributions and probability densities, conditional probability, Bayes formula, mathematical expectation, moments. Part II: Sampling distributions, decision theory, estimation (theory and applications), hypothesis testing (theory and applications), regression and correlation, analysis of variance, non-parametric tests.

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Credit: 3(3-0); ECTS: 8.0

Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.

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Credit: 3(3-0); ECTS: 8.0

This course is a nonmeasure theoretic introduction to stochastic processes, and as such assumes a knowledge of calculus and elementary probability. Some of the theory of stochastic processes is presented and diverse range of its applications is indicated. Outline of Topics: Poisson process, Renewal Theory, discrete-time Markov chains, continuous-time Markov chains, martingales, random walks, Brownian Motion. Applications to queueing and to ruin problems.

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Credit: 3(3-0); ECTS: 8.0

Rationale for Regulating/Supervising Financial Risks. International Regulatory & Supervisory Framework. Quantitative Techniques and Application (based on Excel/VBA/Cyristall Ball). Financial Scandals. Hedge Funds. Project works.

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Credit: 3(3-0); ECTS: 8.0

Introduction to programming in Matlab. Matlab toolboxes related to financial computations. Computations of Probability Distributions in Matlab. Distribution fit. Mixed distributions. Computation of Unconditional and conditional probabilities. Introduction to econometrics. OLS, MLE, properties of the estimators. Autocorrelation-heteroscedasticity-nonlinearity in time series. Time series modeling in Matlab. Commands for AR-MA-ARMA-ARIMA-ARCH-GARCG-Multivariate GARCH modeling. Measuring the risk of foreign exchange, equities, derivatives, bonds. Computation of Zero Coupon Bond-Duration-Convexity-Forward Rate-Yield Curve (Interpolation and function based approaches i.e. Nelson-Siegel). Computation of Portfolio Value at Risk, Covariance VaR, Delta-Normal VaR, Historical Simulation-Filtered Historical Simulation-Bootstrap, Monte Carlo Simulation of Geometric Brownian Motion, CRR, CIR, Vasicek, HJM models.

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Credit: 2(0-2); ECTS: 3.0

Basic concepts, Insurance related institutions, their relations with insurance companies, connection to market and investment tools, the role of laws, regulations, terms and conditions, parties and partners in insurance sector, types of insurance, pricing, product development, managerial and financial operations in an insurance company, investment strategies, financial management in insurance companies.

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Credit: 3(3-0); ECTS: 8.0

Basic concepts of probability in sense of risk theory, Introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurrence process), Convolution and mixed type distributions, Risk models ( individual and collective risk models), Numerical methods ( simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation), Premium calculation principles, Credibility Theory, Retentions and reinsurance, Ruin theory, Ordering of risks.

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Credit: 3(3-0); ECTS: 8.0

Definition of risk, insurance and surety. Risk management techniques and some applications in real life problems. Economic and social significance of insurance. Laws of agency, contract, and negligence and their applications to insurance. Types, scope and organization of insurance companies. Construction of policies including limitations on recovery. Underwriting, marketing, rating and regulation of insurance. Covers the principles of risk management, property-liability insurance and life health insurance. Insurance regulations, laws, and insurance practice in Turkey.

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Credit: 3(3-0); ECTS: 8.0

Essentials of stochastic integrals and stochastic differential equations. Probability distributions and heavy tails. Concepts from insurance and finance. Ordering of risks. Aggregate claim amount distributions. Risk processes. Renewal processes and random walks. Markov chains. Continuous Markov models. Martingale techniques and Brownian motion. Point processes. Diffusion models. Applications to insurance and finance processes.

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Credit: 3(3-0); ECTS: 8.0

Basic concepts, Insurance related Institutions, their relations with insurance companies, connection to market and investment tools, the role of laws, regulations, terms and conditions, parties and partners in insurance sector, types of insurance, pricing, product development, managerial and financial operations in an insurance company, investment strategies, financial management in insurance companies, field trip to insurance companies.

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Credit: 3(3-0); ECTS: 8.0

Mean-Variance (Markowitz) analysis; continuous-time market model in finance; options and exotic options, pricing (valuation) of options; self-financing, optimal strategies, optimal portfolios (problems); martingale method; stochastic control and portfolio optimization.

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Credit: 3(3-0); ECTS: 8.0

Risk rating, Bayes premiums, credibility estimators, large claims and credibility, Buhlman-Straub and other relevant models, hierarchical and multidimensional credibility, linear models, linear trend models, evolutionary models.

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Credit: 3(3-0); ECTS: 8.0

Interest Rate Derivatives: Futures, Options on Bonds, and Options on Interest Rates such as Caps and Floors. Models of Arbitrage-Free pricing of Interest-Rate Derivatives: Arbitrage Pricing Theory for Derivative Securities. Basics for The Modeling of Interest-Rate movements. Dynamics of Interest-Rate movements. Short-Rate Models and the Heath-Jarrow-Morton Model of Forward Rates. Change of Numéraire Technique. Derivation of Formulae for the Pricing and Hedging of Certain Derivatives. Numerical Methods for the Actual Implementation of the Valuation of Term Structure Models.

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Credit: 3(3-0); ECTS: 8.0

Introduction to decision making, expected loss, decision rules and risk, decision principles, utility and loss, prior information and subjective probability, Bayesian analysis, posterior distribution, Bayesian inference, Bayesian Decision theory, minimax analysis, value of information, sequential decision procedures, multi decision problems.

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Credit: 3(3-0); ECTS: 8.0

Basic introduction to simulation concepts, generation of random variants from distributions, test for randomness, Monte Carlo Simulation, selecting input distribution, discrete event simulation, variance reduction techniques, statistical analysis of output.

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Credit: 3(3-0); ECTS: 8.0

Introduction to statistical learning, simulation and supervised learning. Linear methods of regression and classification. Model assessment and selection. Model inference and averaging. Additive models, trees and related methods. Prototype methods and nearest neighbors. Cluster algorithms and support vector machines. Unsupervised learning. Computer applications and MATLAB exercises are important elements of the course.

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Credit: 3(3-0); ECTS: 8.0

Fundamentals of reinsurance including historical development, terminology and distribution systems. Treaty forms, facultative reinsurance, underwriting, rating, accounting and contract issues, analysis of annual statement, testing methods, advanced rating methods in property and casualty excess contracts, analysis accumulations, retention, contract wording and programming.

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Credit: 3(3-0); ECTS: 8.0

Contents vary from year to year according to interest of students and instructor in charge.

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Credit: 3(3-0); ECTS: 8.0

The theory of compound interest: Effective and nominal interest rates, present values, annuities. Survival distributions and life tables. Life Insurance: Level benefit insurance, endowments, varying level benefit insurance. Life annuities. Benefit premiums. Benefit reserves.

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Credit: 3(3-0); ECTS: 8.0

Risk theory for pension funds. Pension schemes for active and retired lives. Valuation of pension plans. Funding Methods: Unit Credit, Attained Age, Entry Age Normal and other Methods. Contributory and Benefit Plans.

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Credit: 3(3-0); ECTS: 8.0

Insurance models including expenses. Special annuities and insurance. Advanced multiple life theory. Population theory. Interest as a random Variable.

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Credit: 2(2-0); ECTS: 6.0

LaTeX and Matlab; Basic Commands and Syntax of LaTeX and Matlab; Working within a Research Group via Subversion; Arrays and Matrices; Scripts and Function in Matlab; Commands and Environments in LaTeX; More on Matlab Functions; Toolboxes of Matlab; Packages in LaTeX; Graphics in Matlab; Handling Graphics and Plotting in LaTeX; Advanced Techniques in Matlab: memory allocation, vectoristaion, object orientation, scoping, structures, strings, file streams.

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Credit: 2(2-0); ECTS: 6.0

Review of Programming and Toolboxes, Packages, Modules; Iterative Linear Algebra Problems; Root Finding Programs; Recursive Functions and Algorithms; Optimisation Algorithms; Data Fitting and Interpolation; Extrapolation; Numerical Integration; Numerical Solutions of Differential Equations: IVPs and BVPs; Selected Topics (algorithms and coding in different fields).

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Credit: 0(0-0); ECTS: 130.0

Program of research leading to Ph.D. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write up of thesis is in progress.

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Credit: 3(3-0); ECTS: 8.0

Risk in insurance systems. Short, medium and long term financial structures of insurance funds. Modelling and valuation of insurance plans. Contribution and benefit schemes for insurance and reinsurance. Economic dynamics, financial markets and assets management for insurance systems. Multiple decrements, actuarial balance and fair premiums.

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Credit: 3(3-0); ECTS: 8.0

Numerical Methods for Discrete Time Models: binomial method for options; discrete time optimal control problems. Reminders on Continuous Models: Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile. Monte Carlo Method for Options: generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method. Finite Difference Methods for Options: explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options. Finite Difference Methods for Control Problems: Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.

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Credit: 3(3-0); ECTS: 8.0

Financial modelling beyond Black-Scholes Model. Stochastic processes. Building Lévy processes. Option pricing with stochastic processes: Stochastic calculus for semimartingales, change of measure, exponential Lévy processes, stochastic volatility models, pricing with stochastic volatility models. Hedging in incomplete markets, risk-neutral modeling. Integro-partial differential equations. Further topics in numerical solutions, simulation and calibration of stochastic processes.

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Credit: 3(3-0); ECTS: 8.0

Globalization techniques, semidefinite and conic optimization, derivative free optimization, semi-infinite optimization methods, Newton Krylov methods, nonlinear parameter estimation and advanced spline regression, multi-objective optimization, nonsmooth optimization, optimization in support vector machines.

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Credit: 3(3-0); ECTS: 8.0

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

See the course in IAM Catalogue or METU Catalogue

Credit: 3(3-0); ECTS: 8.0

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

See the course in IAM Catalogue or METU Catalogue

Credit: 3(3-0); ECTS: 8.0

Basic concepts of probability in connection with Risk Theory; introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurance process); convolution and mixed type distributions; risk models (individual and collective risk models); numerical methods (simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation); premium calculation principles; Credibility Theory; retentions and reinsurance; Ruin Theory; ordering of risks.

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Credit: 3(3-0); ECTS: 8.0

Pricing financial instruments, algorithms and programming. Econometric estimation of the stochastic processes.

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Credit: 3(2-2); ECTS: 8.0

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

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Credit: 3(3-0); ECTS: 8.0

The course will follow two main textbooks and selected articles from scientific journals. Course will be supported by the presentation and speeches of guest speakers. This course discusses financial risk management from the perspective of energy. Course focuses mostly on the energy market, energy trading and energy risk management through various instruments. The topics also cover the interest of hedge funds. A special attention is also given to behavior of energy-dominant sovereign wealth funds.

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Credit: 3(3-0); ECTS: 8.0

The course’s aims consist in a deepened knowledge by he students, and that they are enabled and activated to a do their own scientific work in future. Therefore, the objective of this course is to guide students in their first steps as young researchers on modern areas of mathematical finance. For this purpose, course material will be presented and distributed whose understanding will demand a joint view and participation of the different mathematical foundations of finance. This necessitates further reading and deep reflection by all participants, a spirit of scientific entrepreneurship and willingness to become more mature. Approaches and results of the sources taught and distributed will become improved by the participants, and every participant will prepare a small paper on his/her findings that will be submitted.

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Credit: 3(3-0); ECTS: 8.0

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

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Credit: 3(3-0); ECTS: 8.0

The goal of this course is to establish a well background in this field. The important subjects in this course are stationarity, autocorrelation, partial autocorrelation, ARIMA models, VAR models, cointegration, difference equation and unit roots. Thus, using these concepts, a student can study and analyze the matters in the area of Financial Econometrics.

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Credit: 3(3-0); ECTS: 8.0

Within the context of value maximization, this course focuses at length on a corporations financial risk management needs and techniques. While we pay particular attention to financial institutions, our coverage is general enough for extending its lessons to other corporate entities, including multinationals.

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Credit: 3(3-0); ECTS: 8.0

Generating Random Numbers; Basic Principles of Monte Carlo; Numerical Schemes for Stochastic Differential Equations; Simulating Financial Models; Jump-Diffusion and Levy Type Models; Simulating Actuarial Models; Markov Chain Monte Carlo Methods.

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Credit: 3(0-0); ECTS: 8.0

Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge.

See the course in IAM Catalogue or METU Catalogue

Credit: 3(3-0); ECTS: 8.0

Short review of basic concepts, terminology, definitions in life insurance and the types of life insurance. Product development, pricing strategy, preliminary and final product design, product implementation and management, pricing assumptions and life insurance cash flows, reserves, reinsurance, investment income, profit measurement, financial modeling, asset/liability modeling, and matching, stochastic modeling and financial management.

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Credit: 3(0-0); ECTS: 8.0

Types of pension systems, the nature of interrelationship between social security schemes, their demographic, economic and fiscal environments, the valuation of public pension systems, structural reform considerations, the valuation of short-term cash benefits.

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Credit: 3(3-0); ECTS: 8.0

Forms of survival models, survival distributions, parametric survival models, introduction to demography and life tables, force of mortality, estimation of parametric survival models, actuarial estimation with survival models.

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