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Apportioning of Risks via Stochastic Dominance

29 Pages Posted: 24 Nov 2008  

Louis Eeckhoudt

Facultes Universitaires Catholiques de Mons (FUCAM)

Harris Schlesinger

University of Alabama; CESifo (Center for Economic Studies and Ifo Institute)

Ilia Tsetlin

INSEAD

Date Written: November 2008

Abstract

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] via (N + M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state contingent lotteries in such a way as not to group the two bad lotteries in the same state, where bad is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher order risk effects, such as precautionary effects and tempering effects.

Keywords: downside risk, precautionary effects, prudence, risk apportionment, risk aversion, stochastic dominance, temperance

JEL Classification: D81

Suggested Citation

Eeckhoudt, Louis and Schlesinger, Harris and Tsetlin, Ilia, Apportioning of Risks via Stochastic Dominance (November 2008). CESifo Working Paper Series No. 2467. Available at SSRN: https://ssrn.com/abstract=1306282

Louis Eeckhoudt

Facultes Universitaires Catholiques de Mons (FUCAM) ( email )

Chaussee de Binche, 151
Mons 7000
Belgium

Harris Schlesinger (Contact Author)

University of Alabama ( email )

P.O. Box 870244
200 Alston Hall, Box 870224
Tuscaloosa, AL 35487
United States
205-348-7858 (Phone)
205-348-0590 (Fax)

CESifo (Center for Economic Studies and Ifo Institute) ( email )

Poschinger Str. 5
Munich, DE-81679
Germany

Ilia Tsetlin

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

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