In
this talk, I review some basic propositions of economic theory to illustrate
the interplay of economic intuition and mathematical formalization. I identify mathematical
tools from functional analysis, probability theory, nonstandard analysis and
optimization theory that are used to discuss the relationships between
intuitive ideas such as that between technological efficiency and profit
maximization, and between self-interest and societal interest. In particular, I
discuss the fundamental theorems of welfare economics and the role they play in
providing a case for or against free markets.
Professor
Khan will also give a talk in the Economics Department
Tuesday,
November 22, 2000
On Theories of Asset Pricing
We present a model of a financial market in which naïve diversification, based simply on portfolio size and obtained as a consequence of the law of large numbers, is distinguished from efficient diversification, based on mean-variance analysis. This distinction yields a valuation formula involving only the essential risk embodied in an asset's return, where the overall risk can be decomposed into a systematic and an unsystematic part, as in the arbitrage pricing theory; and the systematic component further decomposed into an essential and an inessential part, as in the capital-asset-pricing model.