Course Description - Business Mathematics
course description

The courses of the program with detailed description:

1st Teaching Period

Introduction to Finance and Financial Mathematics
Leventidis Ioannis (Mandatory)
Cash flows, investments, capital markets. Fundamental theory of interest: capital and interest, compounding, present and future value, annuities, IRR, NPV, investment appraisal. Applications: fixed income securities, valuation, bonds, term structure, forward rates, floating interest bonds. Duration, immunization.
Stochastic processes in finance
Poufinas Thomas (Mandatory)
Introduction: forward and futures contracts, options, other derivative securities. Futures markets and hedging: futures contracts trading and markets, hedging with futures, optimal hedge ratio. Valuation of forward and futures contracts: in zero coupon and coupon asses, commodity futures. Interest rate futures: FRAs, bond futures, hedging tactics. Swaps: mechanism, interest rate and foreign currency swap valuation
Survey of Mathematics for non-mathematics majors
Calculus. Constrained and unconstrained optimization. Survey of Linear Algebra: Real and Complex Vectors, matrices, linear transformations, solution of systems, determinants, eigenvalues and diagonalization. Survey of differential and difference equations.
Survey of Probabilities for non-mathematics majors
Trevezas Samis (Mandatory)
Probabilities and Combinatorics. Borel - Cantelli Lemma, Bayes formula, random variables, cumulation distribution function, Central Limit Theorem, estimators, confindence intervals and hypothesis testing
Information systems
Vassalos Paraskevas (Mandatory)
Fundamental concepts. Management Information Systems. Security and control. Data base theory and applications in Access. Spreadsheets and applications. Introduction to Matlab programming.
Tountas Kanellos (Mandatory)
Economics and Management Ι
Kollias Iraklis (Mandatory)

2nd Teaching Period

Analysis and Probability
Information and σ-algebras, measures and probability measures. Random variables and independence, Lebesgue integral. The Radon Nikodym theorem, equivalent measures, density functions, conditional expectation.
Economics and Management IΙ
Kollias Iraklis (Mandatory)
Consumer behavior, demand functions. Theory of Production, firms. Cost analysis. Perfect competition, monopoly and oligopoly. Strategies in oligopolies. Introduction to risk analysis.
Finance: Portfolia, Options, Cost of Capital
Kenourgios Dimitrios (Mandatory)
Portfolio theory: portfolio return and risk, random returns, random portfolio return. The Markowitz model, with or without a riskless asset. CAPM: Market equilibrium, Capital market line, security market line, valuation through the CAPM. Factor models, arbitrage pricing theory. Utility functions, linear valuation, log optimal pricing, risk neutral pricing.
Advanced Topics in Accounting Operations Research – Mathematical Programming
Economou Antonios (Mandatory)
Problem formulation in OR. Linear programming problems, graphical interpretation. The simplex algorithm. The transportation problem. Nonlinear programming.

3rd Teaching Period

Stochastic Processes
Emmanouil Ioannis (Mandatory)
Martingales and martingale transforms, stopping times and the optional stopping theorem. The discrete market model, completeness and viability, option valuation in incomplete markets, the CRR and UND models, equivalent martingale measures and option valuation.
Derivatives II
Poufinas Thomas (Mandatory)
Actuarial Mathematics: Life Insurances Econometrics
Meligotsidou Loukia (Mandatory)
The linear model – simple and multivariate regression. Extensions of the linear model. Artificial variables. Multicollinearity, heteroscedasticity, autocorrelation. Errors in variables, auxiliary variable. Systems of equations: Introductory concepts, identification, estimation of parameters
Operations Research: Stochastic models, dynamic programming
Trevezas Samis (Mandatory)
Dynamic programming in various contexts. Inventory theory, Markov chains. Markovian Decision processes.

4th Teaching Period

Advanced Topics in Stochastic Processes
Random walks and Brownian motion, stochastic integration and Ito's Lemma, stochastic differential equations.
Mathematical Models in Production and Logistics I
Burnetas Apostolos (Mandatory)
Inventory theory. Continuous and periodic review, under certainty. Stochastic models, continuous review. One period models (newsboy problem)
Actuarial Mathematics: Risk Theory
Cheliotis Dimitrios (Mandatory)
Introduction to risk theory. Single period models. The role of the central limit theorem. Large deviations. Multiperiod models. Introduction to reinsurance.
Meligotsidou Loukia (Mandatory)
Fundamental concepts of time series and forecasting. Stochastic models (AR, MA, ARMA). Box Jenkins forecasting methodologies, ARIMA models. Stationarity, trend, unit root tests. Dynamic multivariate models, VAR models
Institutional Investing
Dotsis Georgios (Mandatory)

5th Teaching Period

Seminar in Insurance Policy
Leventidis Ioannis (Mandatory)
Market risk management: naked and covered positions, stop loss strategies, Greeks, portfolio, insurance. Numerical methods: binomial trees, Monte Carlo simulation, variance reduction, finite difference methods. Interest rate derivatives: embedded options, MBSs, OAS, lack’s mode, Caps, Swaptions, Accrual Swaps, spread options. Term structure models and valuation of interest rate options: equilibrium models, one factor models, two factor models, no arbitrage models, interest rate trees. Exotic options
Mathematical Models in Production and Logistics II
Fundamental concepts: workstation, routing, throughput, work in progress, cycle time. Fundamental parameters: bottleneck rate, raw process time,critical WIP. Little’s law and the study of production lines. Effect of randomness – variability in production lines. Introduction to queuing. Markovian queues of M/M/1 and M/M/m types and generalizations. Non-Markovian queues. Networks of queues.
Seminar in Operations Research
Presentations by invited speakers. Indicative topics: Data envelope analysis and its applications. Dynamic optimization and applications to optimal economic growth. Supply chain analysis. Introduction to revenue management.
Research Method Seminar
Transactional information systems
Vassalos Paraskevas (Mandatory)
Data base theory. E- R diagrams, the relational model, introduction to SQL. Transactions theory: concurrent transactions, possible problems. Serializable schedules, deadlocks, two phase locking.

6th Teaching Period

Advanced topics in Actuarial Mathematics
Rationale and fundamental concepts of reinsurance. Reinsurance schemes and their mathematical analysis. Reinsurance contracts and their terms. Calculation of reinsurance rates and portfolio valuation. Reinsurance in general insurance and life insurance
Seminar in Finance
Risk Management: Economic capital, RAROC. Market risk management, Value at Risk. Asset Liability Management. Introduction to credit risk and its management.
Games and Bargaining
Mageirou Evangelos (Mandatory)
Decision theory: Decision trees. Elementary utility theory, subjective probability. Application to portfolio theory. Game theory: Combinatorial games. Information sets. Normal and extensive form. Dominant solutions. Nash equilibria. Zero and nonzero sum games. Nash Bargaining. Optional: bargaining game.
Advanced topics in Operations Research
Τopics depend on the interests of students and the instructor. Indicative topics: Applications in Linear Programming Network Optimization Models Integer Programming
Marketing Models
Burnetas Apostolos (Mandatory)
Mathematical models for various decision making problems in marketing. Consumer behavior: NBD models, Zero order and Markovian models. Utility models. Pricing models, yield management. Distribution. Advertising and promotion.
Mathematical Models in Production and Logistics III
Structural reliability. Reliability of systems with independent units – exact calculations. Reliability of systems with independent parts - bounds. Structural and reliability importance. Lifetime distributions. Mean time to failure. Renewable reliability systems. Applications.
Mathematical Models in Administration Seminar in Bank Quantitative Management
Balance sheet evolution of a new bank, identification of associated risks, the role of Central Bank, bank products, determination and measurement of Interest Rate Risk on Banking Book (IRRBB), liquidity risk analysis and management (maturity ladder, ways to gain liquidity), market risk measurement and management, Value at Risk calculation (delta VaR, historic simulation), example of CreditVaR calculation according to CreditMetrics methodology, loan provisioning according to ECB methodology for AQR (going concern, gone concern cases), operational risk management, capital adequacy.
Seminar in Management – Introduction to Transactions Law
Stock market law. Investment services and financial markets. The Athens Stock Exchange. Clearing in the ASE. Information Bulletin. Market abuse: Market manipulation and insider trading.