EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 161
THE OPTIMAL ALLOCATION
OF RISKS UNDER
PROSPECT THEORY
BY LIVIO STRACCA
July 2002
EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 161
THE OPTIMAL ALLOCATION
OF RISKS UNDER
PROSPECT THEORY
BY LIVIO STRACCA*
July 2002
* European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany. Email: [email protected]. I thank a referee for many
useful suggestions. Moreover, I thank Ali al-Nowaihi, David Fielding, Kevin Lee, Panicos Demetriades and other participants in a seminar
at the University of Leicester. Any remaining errors in the paper are only the author’s responsibility.
© European Central Bank, 2002
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All rights reserved.
Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.
The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank.
ISSN 1561-0810
Contents
Abstract
4
Executive summary
5
1
Introduction
7
2
The optimal allocation of risks under cumulative prospect theory 9
2.1 The environment
9
2.2 The prospective value function for the problem
10
2.3 Conditions for optimal risk concentration or diversification 13
3
The more general case
19
4
Prospect theory: a solution to the “home bias” puzzle?
22
5
Conclusions
23
References
25
European Central Bank working paper series
28
ECB • Working Paper No 161 • July 2002
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ECB • Working Paper No 161 • July 2002
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23
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ECB • Working Paper No 161 • July 2002
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ECB • Working Paper No 161 • July 2002
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ECB • Working Paper No 161 • July 2002
129 “Non-standard central bank loss functions, skewed risks, and certainty equivalence” by
A. al-Nowaihi and L. Stracca, March 2002.
130 “Harmonized indexes of consumer prices: their conceptual foundations” by E. Diewert,
March 2002.
131 “Measurement bias in the HICP: what do we know, and what do we need to know?” by
M. A. Wynne and D. Rodríguez-Palenzuela, March 2002.
132 “Inflation dynamics and dual inflation in accession countries: a “new Keynesian”
perspective” by O. Arratibel, D. Rodríguez-Palenzuela and C. Thimann, March 2002.
133 “Can confidence indicators be useful to predict short term real GDP growth?” by
A. Mourougane and M. Roma, March 2002.
134 “The cost of private transportation in the Netherlands, 1992-1999” by B. Bode and
J. Van Dalen, March 2002.
135 “The optimal mix of taxes on money, consumption and income” by F. De Fiore and
P. Teles, April 2002.
136 “Retail bank interest rate pass-through: the new evidence at the euro area level” by
G. de Bondt, April 2002.
137 “Equilibrium bidding in the eurosystem’s open market operations” by U. Bindseil, April
2002.
138 “New” views on the optimum currency area theory: what is EMU telling us?” by
F. P. Mongelli, April 2002.
139 “On currency crises and contagion” by M. Fratzscher, April 2002.
140 “Price setting and the steady-state effects of inflation” by M. Casares, May 2002.
141 “Asset prices and fiscal balances” by F. Eschenbach and L. Schuknecht, May 2002.
142 “Modelling the daily banknotes in circulation in the context of the liquidity management of
the European Central Bank”, by A. Cabrero, G. Camba-Mendez, A. Hirsch and F. Nieto,
May 2002.
143 “A non-parametric method for valuing new goods”, by I. Crawford, May 2002.
144 “A failure in the measurement of inflation: results from a hedonic and matched experiment
using scanner data”, by M. Silver and S. Heravi, May 2002.
145 “Towards a new early warning system of financial crises”, by M. Fratzscher and M. Bussiere,
May 2002.
146 “Competition and stability – what’s special about banking?”, by E. Carletti and P. Hartmann,
May 2002.
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147 “Time-to-build approach in a sticky price, stricky wage optimizing monetary model, by
M. Casares, May 2002.
148 “The functional form of yield curves” by V. Brousseau, May 2002.
149 “The Spanish block of the ESCB-multi-country model” by A. Estrada and A. Willman, May
2002.
150 “Equity and bond market signals as leading indicators of bank fragility” by R. Gropp,
J. Vesala and G. Vulpes, June 2002.
151 “G-7 inflation forecasts” by F. Canova, June 2002.
152 “Short-term monitoring of fiscal policy discipline” by G. Camba-Mendez and A. Lamo, June
2002.
153 “Euro area production function and potential output: a supply side system approach” by
A. Willman, June 2002.
154 “The euro bloc, the dollar bloc and the yen bloc: how much monetary policy independence
can exchange rate flexibility buy in an interdependent world?” by M. Fratzscher, June 2002.
155 “Youth unemployment in the OECD: demographic shifts, labour market institutions, and
macroeconomic shocks” by J. F. Jimeno and D. Rodriguez-Palenzuela, June 2002.
156 “Identifying endogenous fiscal policy rules for macroeconomic models” by J. J. Perez,
and P. Hiebert, July 2002.
157 “Bidding and performance in repo auctions: evidence from ECB open market operations”
by Kjell G. Nyborg, Ulrich Bindseil and Ilya A. Strebulaev, July 2002.
158 “Quantifying Embodied Technological Change” by Plutarchos Sakellaris and D. J. Wilson,
July 2002.
159 “Optimal public money” by C. Monnet, July 2002.
160 “Model uncertainty and the equilibrium value of the real effective euro exchange rate” by
C. Detken, A. Dieppe, J. Henry, C. Marin and F. Smets, July 2002.
161 “The optimal allocation of risks under prospect theory” by L. Stracca, July 2002.
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ECB • Working Paper No 161 • July 2002