Risk minimization and optimal derivative design in a principal agent game |
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Authors: | Ulrich Horst Santiago Moreno-Bromberg |
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Institution: | (1) Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany;(2) Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada |
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Abstract: | We consider the problem of Adverse Selection and optimal derivative design within a Principal–Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her
risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her
income to individual agents. The agents have mean–variance preferences with heterogeneous risk aversion coefficients. An agent’s
degree of risk aversion is private information and hidden from the principal who only knows the overall distribution. We show
that the principal’s risk minimization problem has a solution and illustrate the effects of risk transfer on her income by
means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (in Financ Stochast 9, 269–298, 2005)
and Carlier et al. (in Math Financ Econ 1, 57–80, 2007).
We thank Guillaume Carlier, Pierre-Andre Chiappori, Ivar Ekeland, Andreas Putz and seminar participants at various institutions
for valuable comments and suggestions. Financial support through an NSERC individual discovery grant is gratefully acknowledged. |
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Keywords: | Optimal derivative design Structured securities Adverse selection Risk transfer |
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