The Economics of Risk and Time
Christian Gollier
GREMAQ and IDEI, University of Toulouse
May 27, 1999
2
Contents
I General theory
11
1 The expected utility model
13
2 Some basic tools
23
3 Risk aversion
43
4 Change in risk
65
II The standard portfolio problem
79
5 The standard portfolio problem
81
6 The equilibrium price of risk
95
III Multiple risks
103
7 Risk aversion with background risk
105
8 The tempering effect of background risk
115
9 Taking multiple risks
131
10 Horizon length and portfolio risk
143
11 Special topics in dynamic finance
163
3
4
CONTENTS
IV The complete market model
181
12 The demand for contingent claims
183
13 Properties of the optimal behavior with complete markets
191
V Consumption and saving
199
14 Consumption under certainty
201
15 Precautionary saving and prudence
217
16 The equilibrium price of time
233
17 The liquidity constraint
253
18 The saving-portfolio problem
265
19 Disentangling risk and time
277
VI Equilibrium prices of risk and time
285
20 Efficient risk sharing
287
21 The equilibrium price of risk and time
299
22 Searching for the representative agent
313
VII Risk and information
325
23 The value of information
327
24 Bibliography
355
CONTENTS
5
Introduction
Uncertainty is everywhere. There is no field in economics in which risk is
not an important dimension of the decision-making environment. The theory of
finance provides the most obvious example of this. Similarly, most recent de-
velopments in macroeconomics have been made possible by recognizing the im-
portance of risk in explaining individual decisions. Consumption patterns, invest-
ments and labor decisions can only be understood completely if uncertainty is
taken into account into the decision-making process. Environmental economics
provides another illustration. Public opinion is now very sensitive to the presence
of potentially catastrophic risks related, for example, to the greenhouse effect and
genetic manipulations. Environmental economists introduced probabilistic sce-
narios in their models to exhibit soci