Math-581.Ê Risk Management II:Ê Portfolio Selection and Other Features of Finance Markets.

The course concerns financial markets, and deals, in particular, with such notions as

á Market of random assets;

á Equilibrium in the market of random assets;

á Portfolio selection and optimal behavior in the financial market in the one-period and dynamic frameworks as well;

á 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).

ÊÊÊÊ 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.

3. The Kuhn-Tucker theorem and an interpretation of Lagrange multipliers. The Kuhn-Tucker theorem and the financial market.

4. The equilibrium in the financial market, and equilibrium prices.

5. The Capital-Asset-Pricing Model. Betta and Alpa of a portfolio.

6. Factor models. Arbitrage pricing theory.

7. Expected utility maximization for one period.

8. Expected utility maximization in the continuous time model. Mertonâs formulas.

9. Multiperiod expected utility maximization, and dynamic portfolio optimization.

10. The maximum-expected-log approach.

References:Ê

1. Financial Economics,Ê Ed. Panjer, 1998, The Actuarial Foundation.

2. Ingersol, J.E.ÊÊ Theory of Financial Decision Making, 1987, Rowman & Littlefield Publishers.

3. Bodie, Z., and Merton, R. Finance, 2000, Prentice Hall.

4. Merton, R.Ê Continuous time finance, 1992, Blackwell Publishes.

5. Duffie, D. Asset pricing theory. 1992,Ê Princeton:Princeton Univ.Press.