The course will provide the student with the tools to analyze producer decision making in an uncertain decision setting. Students will study producer decision making
in a unified framework that emphasizes the common structure underlying modern decision theory, asset pricing in financial markets, and the Arrow-Debreu state space approach to production under uncertainty.

Uncertain production decisions will be studied as a particular type of asset allocation decision in a finance economy setting. Both producer preferences and the production technology will be studied in general frameworks that allow for discrimination between Knightian risk and uncertainty and that accommodate behavior consistent with both the Ellsberg Paradox and the Allais Paradox.

Lecture Topics

• State space representation of uncertainty
• Preferences under uncertainty and the distinction between risk and uncertainty
• Representing production technologies and financial markets in an uncertain setting
• Duality theory for stochastic production technologies
• Optimal production and portfolio decisions in an uncertain setting
• The cost-based (no production/financial arbitrage) approach to asset pricing

Practical Session Topics

• Choice among risky alternatives in an experimental setting and the Allais Paradox
• Choice among uncertain alternatives in an experimental setting and the Ellsberg Paradox
• Cost function estimation in an uncertain setting
• Data envelopment analysis representation of stochastic technologies
• Estimation of stochastic discount factors from cost-based asset pricing models

Course Outline

Day 1 will be devoted to developing the state/act representation of an uncertain decision setting that underlies both modern decision theory and financial market analysis. Starting with preference orderings over uncertain outcomes, both complete and incomplete models of decision maker objective functions will be studied. The subjective expected utility model, and its weaknesses, will be studied. Laboratory experiments will be used to illustrate the implications of the Allais Paradox for individual decision making.

Day 2 focuses on generalizations of the subjective expected utility model and the distinction between Knightian risk and uncertainty. Preference structures studied will include the rank-dependent expected utility model and generalized expected utility models, such as the maximin expected utility model, that accommodate behavior consistent with the Ellsberg Paradox. Incomplete preference structures will also be considered and functional representations of them will be derived. Laboratory experiments will be used to study and illustrate the implications of the Ellsberg Paradox.

Day 3 lectures will introduce the elements of a finance economy with real, but stochastic, production possibilities in a two-period Arrow-Debreu setting. The key role that cost minimization plays in a stochastic setting for producers with general monotonic preference structures (including subjective expected utility and its generalizations) will be developed and the use of derivative-cost functions in detecting the presence or absence of both financial arbitrages and arbitrages between real production possibilities and financial markets will provide the unifying topic for this day’s lectures. The restrictions that the absence of arbitrage places on the derivative-cost function , its differential representations, and their relation to no-arbitrage pricing are among the topics to be covered.

Day 4 will be devoted to studying the duality between stochastic production technologies and cost structures. The role of various restrictions on the technology, such as homotheticity and separability, in identifying and facilitating econometric estimation of cost structures dual to the primal technology will be studied.

Day 5 is dedicated to developing a simple, but econometrically implementable, approach for generating stochastic discount factors from the derivative cost function. The role of the stochastic discount factor in pricing both financial assets and real, but stochastic, options as well as other financial instruments will be studied.

Texts

The material for lectures will be drawn from 3 main sources:

Magill, M. and M. Quinzii. Incomplete Markets Vol. 1. MIT Press, Cambridge, 1996.

Chambers, R.G. and J. Quiggin. Uncertainty, Production, Choice, Uncertainty, and Agency: The State-Contingent Approach. Cambridge University Press, New York, 2000.

Gilboa, I. Theory of Decision under Uncertainty. Cambridge University Press, New York, 2009.