Master of Science in Mathematics,
Risk Analysis and Management Track

12 three credit graduate courses, and one optional elective during the last semester of the program. The degree will be completed in 12 months. Full-time students will take four courses per semester to complete the program in three semesters. See Course Requirements below for the course offering per semester. 
 

Course requirements

Fall term

1. Risk Analysis and Management 1 (RAM1)
2. Corporate Finance (FIN 6428)
3. Introduction to quantitative Risk Analysis and ManagementIt
4. Probability for Finance



Spring term

1. Stochastic Calculus
2. Risk Analysis and Management 2 (RAM 2)
3. C++ for Risk Analysis and Management (COP 6007)
4. Numerical Methods (in Risk Analysis and Management) (MAD 5405)



Summer term

1. PDE for Risk Analysis and Management.
2. Risk Analysis and Management 3 (RAM 3)
3. Special Topics, STA 6930. This is a course on Time Series Analysis
4. Choose one from:

FIN 6487 Financial Risk Management
or
FIN 6538 Financial Futures and Fixed Income Investments 
 

Remark: This exact order that the courses are given might be changed  for scheduling purposes.
 

Short descriptions of all the courses in the program.
 

RAM 1:  Basic concepts of probability, Introduction to measure theory, Riemann integral, Lebesgue Integral,  conditional expectation, Borel-Cantelli lemma, notions of convergence, characteristic functions, Limit theorems: law of large number, central limit theorem, Markov chains: discrete and continuous time Markov chains, Random walks, Gaussian stochastic processes, Martingales, Binomial model of asset pricing, Lognormal model of asset prices, Black-Scholes Model, derivation of the Black-Scholes equation, Black-Scholes formula for European option prices, Hedging parameters: the Greeks (Delta, Gamma, Vega, Theta) , American options. Early exercise and time-optionality

FIN 6428: Corporate Finance. See description in FIU’s  graduate catalog.

COP 6007: See description in FIU’s  catalog.

Stochastic Calculus: Basic examples of risk management derivatives, Discrete time models: Single period models, pricing a European option, characterizing no arbitrage, risk neutral probabilities. Brownian motion,  Martingales in continuous time, Stochastic Integration: Ito’s Integral, Ito’s Formula, Martingale Representation Theorem , Stochastic Differential Equations: Existence and Uniqueness Theorem, Ornstein-Uhlenbeck Processes, The Diffusion Equation: Markov property, Strong Markov property,  Generator of an Ito Diffusion, American securities, Girsanov Theorem, Arbitrage and SDE: Black-Scholes Model; Black-Scholes Formula.

RAM 2: Discrete and continuous time models, Applications of the discrete versions of the stochastic integrals and Ito’s lemma to risk analysis and management. Arbitrage based pricing of derivative securities. Risk neutral valuation, Binomial trees and American options, Black-Scholes and extensions, Some exotic options.

Numerical Methods in RAM: Review of the standard numerical analysis, Numerical differentiation and integration (some useful quadrature methods). Numerical solutions of non-linear equations (Newton’s and other methods). Numerical solutions of ODEs and PDEs (Runge-Kutta, Crank-Nicholson, Finite difference). Binomial and trinomial tree methods (with applications to finance, such as pricing American options). Introduction to Monte Carlo (variance reduction) and quasi Monte Carlo, with applications in financial asset pricing.

PDE in RAM: Deterministic and stochastic optimization. Dynamic programming. Hamilton-Jacobi equations. Forward and backward Kolmogorov equations. Feynman-Kac formula. Green’s function.

RAM 3: Continuous time risk analysis and management. Arbitrage pricing theory (Harrison-Kreps style) in continuous time with appropriate mathematical precision. Exotic options such as compound options, quantos, basket and barrier options, etc. Interest rate models (Heath-Jarrow-Morton, Hull-White, etc), yield curves, and pricing of interest rate derivatives (swaps, swaptions, caps, etc).

Special Topics, STA 6390: Topics in econometric theory and methods used in the empirical analysis of risk management time series (there will be some coverage of traditional statistical methods used in the analysis of risk analysis cross-sectional data).

The course will have two major parts:

Part 1 will cover the essentials of time series models useful in analysis risk analysis time series [ARFIMA, regression, basic non-linear (ARCH-GARCH models, bilinear), vector ARIMA, unit roots and co-integration, advanced non-linear]

Part 2 will cover the econometric theory and applications of important models in finance [CAPM, multifactor pricing, tests for asset predictability, long-memory, term structure, derivative pricing, etc.]. All aspects of the theory will be put to practice at computer lab sessions using computer software and actual risk management data. 

Securities Analysis (FIN 6515). See FIU catalog, or  FIN 6426: Financial Management Policies: See description in FIU’s graduate catalog.

List I 

Optimization and Linear Algebra: Basic linear algebra. Topological concepts, convexity. Simplex Method, unconstrained linear problems, descent methods, contrained linear problems, Langrange methods,Kuhn-Tucker techniques.

MAA 5616: See FIU’s catalog.

STA 6326: See FIU course catalog

STA 3033: See FIU course catalog
 
 

For more information, contact:

Professor Enrique Villamor, Program Director, Risk Analysis & Management, Mathematics, Florida International University at (305) 348- 2056 or via email at villamor@fiu.edu