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Notes

These notes are mainly written for my own use, but you're welcome to take a look and see if you find anything useful. The notes are not copyrighted, but if you use them in a presentation or a publication, I think it's only fair to mention me.

  • Conditional Probability Theory
    All pretty standard, yet useful stuff: the geometric interpretation of conditional expectation, and the law of iterated expectations and the EVE formula. I included some applications to normal linear regressions, and to dynamic Gaussian updating.
  • The Bellman Principle of Optimality
    I try to make sense of the Bellman principle of optimality in both discrete and continuous time, and under both certainty and uncertainty. I analyze the conditions in which the Bellman principle can be applied. As a bonus, I use the Bellman method to derive the classical Euler-Lagrange equations of variational calculus.
  • Consumption-Investment Problems for CARA Agents
    I compute the optimal consumption and portfolios of investors with constant absolute risk aversion (CARA) utility. I do that in infinite horizon, in both discrete and continuous time. The computations are all standard, and can be found e.g. in Ingersoll. I do them in somewhat more detail (although without much intuition).
  • Walrasian Equilibria and Rational Expectations Equilibria
    I discuss asymmetric information and some fundamental equilibrium concepts: the Walrasian Equilibrium (WE), the Rational Expectations Equilibrium (REE), the Noisy REE, and the Differential Information REE. The notes include a small discussion on the Grossman--Stiglitz paradox, and the No-Trade Theorem of Milgrom and Stokey. These notes were inspired by Dimitri Vayanos's MIT PhD class notes - I hope he'll publish them at some point!
  • Uniqueness of Equilibrium in the Kyle (1985) Model
    There is clearly a unique linear equilibrium in the single period Kyle (1985) model. But is this the only equilibrium if the insider can choose nonlinear strategies? This problem is suprisingly complicated. I was not able to solve it, but in this note I show how to reduce the problem to an equivalent mathematical statement (a "conjecture") that can hopefully be proved one day. I know that Alex Boulatov, Dmitry Livdan and Johan Walden made some progress in this problem (and they are not the only ones), but to my knowledge the problem is still open.

Below are some papers on subjects that interested me at some point. I'm not particularly fond of these papers anymore (if I ever was), but who knows, one may still find something interesting in there.

  • Post-Socialist Transition: Romania and Poland (May 2002)
    This is a paper I wrote for the Socialism and Post-Socialist Transition class I took at Harvard in the Spring of 2002. It happened to be the last course taught here by Janos Kornai, the great Hungarian analyst of the socialist system. My paper however is far from great.
  • Comments on Prospect Theory (January 2000)
    This is my reaction to Kahneman and Tversky's prospect theory (an alternative to classical utility theory). As you can see if you read my note, I don't believe one can make Prospect Theory coherent, although the intuition that generated their paper is pretty useful.

And here is a little essay I wrote about economic research: