Scientific Program > Topic 3 > Session 3O >
Presentation 3O3. Teaching Stochastic Calculus to the 3rd Year Students

Presenters
R. Guo (South Africa) rguo@maths.uct.ac.za
Tim Dunne (South Africa)
 
G. Tucker (South Africa)  

 

Presentation Abstract
In this presentation, we offer our past four years' experiences on the painful task of teaching stochastic calculus. The material was traditionally offered to postgraduates worldwide but at University of Cape Town we had to teach the third year actuarial science students. Stochastic calculus is in general regarded as the cornerstone of modern investment and insurance theory. At its introductory level, stochastic calculus involves topics such as s-algebras, probability spaces, measurable functions, filtrations, stopping times, conditional expectation given a ?-algebra, martingales, Brownian motion, Ito integrals, Ito formulae, Ito stochastic differential equations and related insurance and investment applications. However, even at its elementary level, the teaching task was nonetheless problematic. In the past, Subject 103 defined by Institute of Actuaries merely required us to teach discrete-time as well as continuous Markov chains and time series analysis. But the Institute changed the Core Reading of Subject 103 substantially about four years ago. The Core Reading itself and the Institution examination papers appeared to conflict with each other. It seemed that the Core Reading only requires some basic probability theory, Newton calculus and Riemann integration theory as its mathematical foundation. The examination paper, however, requires quite deep knowledge of real analysis and some knowledge of measure theory. In the face of such an apparent controversy and unthinkable teaching task, the question of balancing the Institution's target with the students' reality was the major concern of our last four years' experience. In our course STA 344S Stochastic Analysis (STA 313), we covered all the related concepts and theorems listed in the Core Reading, aiming at full compliance with the target set by the Institution of Actuaries. When we organized our teaching structure, we put our best efforts in presenting our materials mostly on advanced calculus (mathematical analysis) base. On the other hand, we were trying to motivate our students to participate in the learning process. We believed that learning should be a double input and interaction process. We used a project, homework exercises and regular class tests to continuously assist students to feel their progress and discover their weaknesses. Furthermore we experimented with a feedback mechanism - a Class slip card. In terms of the card system, each student's weekly submission had to be signed by class representative each class and included their self-evaluations as well as teaching evaluations. Based on year 2001 data collection, we use fuzzy analysis for a comprehensive evaluation of the teaching quality of our course STA 344S.

 

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