Introduction to Analytical Programming and Numerical Methods
Admission to the MRM program or consent of the instructor
This course is an introduction to analytical programming and numerical methods. The objective is to learn how to develop algorithms and computer code for scientific computing with a view towards the practical application of mathematical models in risk management, insurance, economics, finance, and related fields. The course emphasizes the principles and numerical techniques used to turn algorithms into reliable and efficient computer programs.
This course introduces stochastic models for risk manage- ment, broadly defined. The course has two main components. The first component covers single-period models including severity models, frequency models, compound distributions, and aggregate loss models. The second component covers multi-period models by intro- ducing stochastic processes with emphasis on Markov chains, Poisson processes, and Brownian motion. Applications to insurance appear throughout the course. The second component adds applications to finance such as the Black/Scholes/Merton model and credit loss models.
This course provides a rigorous introduction to financial economics. The course is comprised of three main components. The first is the analysis of individual behavior under uncertainty and its implications for individual portfolio choice and the demand for insurance in both static and dynamic settings. The second component introduces students to the equilibrium approach to pricing determination in securities and insurance markets. The final section focuses attention on the valuation of interest-rate dependent assets.
This course introduces students to continuous-time financial models essential for the practice of mathematical risk management. It begins with a discussion of the funda- mental mathematical tools from continuous-time stochastic processes including Ito’s formula, change of measure, and martingales. This provides a framework for financial con- cepts including hedging, complete markets, and incomplete markets. The mathematical tools and financial concepts are applied to the risk management and valuation of finan- cial derivatives based on stocks and bonds, separately, and insurance company liabilities with embedded financial options. The course concludes with a consideration of models that jointly value stocks, bonds and non-traded assets.
Emphasis is on the development of “hands-on” experience which includes the calibration of models and dis- cussion of the data issues faced in the application of these models. This course is intended for all students considering a career in quantitative risk management, whether in the in- surance, banking, or non-financial sector.
This course provides a detailed study of pricing of interest rate securities based on stochastic term structure models. A review of stochastic calculus is given; short rate and HJM models are introduced, developed and compared; finally credit risky securities are studied.