Math-581. Risk Management II:
Portfolio
Selection and Other Features of Finance Markets.
The teaching
material presented below may change from semester to semester.
Instructor: Professor Vladimir Rotar; Office GMCS-514, phone: 594 7244; e-mail: rotar@sciences.sdsu.edu or vrotar@euclid.ucsd.edu.
The course concerns
financial markets, and deals, in particular, with such notions as
· Market of random assets;
· Equilibrium in the market of
random assets;
· Portfolio selection and
optimal behavior in the financial market in the one-period and dynamic
frameworks as well;
· Analysis of financial markets.
The prerequisite is ordinary calculus (not complicated, but
a student should be able, for example, to differentiate simple functions, and
to know what the number e is), and an introductory course of Probability
Theory (say, Stat-550 or Stat-551a are more than enough).
The course is self-contained; in particular
Math-580, or Math-544 are NOT needed.
List of Topics.
1.
Introduction. Revision: multivariate
probability distributions; covariance and correlation; multivariate normal
distribution. Method of principal components.
2.
Markets of random assets. The Markowitz Model. Efficient portfolios. The Kuhn-Tucker
theorem and an interpretation of Lagrange multipliers. The Kuhn-Tucker
theorem and the financial market.
3.
The equilibrium in the financial market,
and equilibrium prices.
4.
The Capital-Asset-Pricing Model. Beta and Alpha of a
portfolio.
5.
Factor models. Arbitrage pricing theory.
6.
Expected utility maximization for one
period.
7.
Expected utility maximization in the
continuous time model. Merton’s formulas. Multiperiod
expected utility maximization, and dynamic portfolio optimization.
8.
The maximum-expected-log approach.
References:
1.
Financial Economics, Ed. Panjer, 1998, The Actuarial Foundation.
2.
Ingersol,
J.E. Theory of Financial Decision
Making, 1987, Rowman & Littlefield Publishers.
3.
Bodie, Z.,
and Merton, R. Finance, 2000, Prentice Hall.
4.
Merton,
R. Continuous time finance, 1992,
Blackwell Publishes.
5.
Duffie, D. Asset
pricing theory. 1992,