Mathematical finance - Lezione (2007/2008)

Learning outcomes

This course is in two parts. The first part provides the mathematical models to analyze some general issues related to finance. The second part is focused on some important issues in corporate finance, such as capital budgeting choices and real options theory and capital structure choices.

Part I: Theory of Finance
1. Investment, consumption, and the role of financial markets.
2. Choices under uncertainty. Expected utility theory. Risk aversion, risk premium, stochastic dominance and mean-variance choices.
3. State-preference theory. Determinants of asset prices. Beta-valuation and risk-neutral valuation.
4. Equilibrium asset pricing models: CAPM and APT.

Part II: Corporate Finance
5. Basics of stochastic calculus and dynamic programming
Binomial process, Brownian motion. Dynamic programming and Bellman principle. Optimal stopping problems. Stopping region and continuation region. Ordinary differential equations. Smooth pasting and value matching.
6. Capital Budgeting: Corporate investment under certainty. Fisher separation theorem. Maximizing equity value and NPV. Corporate investment under uncertainty: Fama (1977). Certainty equivalent. Limitations of NPV under uncertainty and with managerial flexibility: real options. The option to defer an investment. The option to abandon a business. The option to switch.
7. Capital structure: The value of the firm and capital structure with taxes: Modigliani and Miller (1958,1963). Average cost of capital. Separation between investment and financing decisions. Extensions: Hamada (1969), Rubinstein (1973), Merton (1974). Personal taxes and capital structure: Miller (1977). Agency costs of debt. A dynamic model of capital structure: Leland (1994).

Students obtain the final grade by doing the homework assigned during classes and by making a presentation at the end of the course.