# SFB 303 Discussion Paper No. A - 192

**Author**: Duffie, Darrell, Wayne Shafer, David Cass, Michael Magill, Martine Quinzii, and John Geanakoplos

**Title**: Lecture Notes in Incomplete Markets

**Abstract**: The Bonn Workshop of 1988 has focused on the study of incomplete security markets, which extends the
standard theory of competitive economic behavior to settings in which there are uninsurable risks, given only the
currently available financial markets. The following five pieces summarize a corresponding series of five lectures
held at the beginning of BoWo '88 with the purpose of communicating some of the basic issues and results on
incomplete security markets to a broad spectrum of students and researchers in this and other areas of
economics. Wayne Shafer: Lecture 1 -IntroductionIn the Arrow-Debreu model of an economy it is assumed that
there are markets for all commodities - also for those to be delivered at future dates in uncertain events. In such
a situation all economic decisions will be made at one time, markets will open only once and consequently
consumers will face a single budget constraint. For reference see Debreu (1959) especially chapter 7. In this
series of lectures, however, we will drop the assumption of a complete market structure. Then there will be
active markets at future dates and agents will face a sequence of budget constraints. Since an agent's utility
depends on consumption of current and future goods, expectations about future states and future prices will
affect agents' plans, i.e. his/her demand or delivery of current and future goods and assets. What would be an
equilibrium in this context? As a solution concept to the equilibrium problem we use the perfect foresight
approach. An equilibrium will therefore consist of a consumption plan for each agent, which is optimal in his/her
budget set, spot prices for current and future consumption, and asset prices such that all markets clear and
agents' price expectations are borne out in equilibrium. David Cass: Lecture 2 -The Basic Model with Assets
with Exogenously Determined ReturnsAs the following analysis will show, the incomplete markets model with
purely financial assets is in many ways very similar to the standard Walrasian model, with two main differences:
- consumers face multiple "real" budget constraints, - there are additional "price" parameters (or variables, for
example, asset prices) which do not appear in the Walrasian model. As far as existence of equilibrium is
concerned these differences do not really matter: Equilibria exist under fairly standard assumptions. The first
part of this talk will indicate why this is true. However, as far as determinacy of equilibrium is concerned there is
a major difference with the Walrasian model: Quite generally, instead of a finite number of equilibrium
allocations we will get a tremendous degree of real indeterminacy in the incomplete markets case; the exact
degree will depend on what we consider as parameters (or variables) of the model. These results will be sketched
in the second part of the talk. Finally, let it just be noted here that another motivation for studying incomplete
market models with nominal assets is, that they allow for sunspot activity to influence the real
allocations. Michael Magill: Lecture 3 -Equilibrium with Financial Markets. This lecture considers a general
model of equilibrium with financial markets for a stochastic exchange economy with two periods, I agents and L
goods. Uncertainty arises due to S possible states of nature at date 1. Note that this economy generalises easily to
an economy with a T period eventtree. Each agent i is characterised by a smooth utility function, and a
nonnegative vector of initial endowments. Therefore our stochastic exchange economy depends on the utility
function and the initial endowments of each agent. Martine Quinzii: Lecture 4 -Production and the Behavior of
the FirmThe main purpose of this talk is to add production to the model considered so far and to analyse the
consequences of the assumption of incomplete markets on the production decision of forms and the efficiency of
a competitive stock market equilibrium. John Geanakoplos: Lecture 5 -An Application of the Incomplete Markets
Model to Finance: The Capital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) allows us to give
interesting answers to questions such as: What is the meaning of risk? How does the market price risk? If all
markets are efficient, can some stocks promise a higher return than others? What is meant by efficiency? No
arbitrage? What is the role of the riskless asset? In the following the CAPM will be presented as a special case of
the basic model given in lecture 1 and the standard theorems which answer the just outlined questions will be
derived in this context.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: September 1988

Unfortunately this paper is not available online. Please contact us to order a hardcopy.
SFB 303 Homepage

21.10.1999, Webmaster