Prospect and Markowitz stochastic dominance

W. K. WONG; R. H. CHAN

doi:10.1007/s10436-007-0072-4

Prospect and Markowitz stochastic dominance

W. K. WONG^*, R. H. CHAN

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

64 Citations (Scopus)

Abstract

Levy and Wiener (J Risk Uncertain 16(2), 147-163, 1998), Levy and Lev y (Manage Sci 48(10), 133-1349, 2002; Rev Fin Stud 17(4), 1015-1041, 200 4) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be 'the opposite of' or 'the same as' their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.

Original language	English
Pages (from-to)	105-129
Number of pages	25
Journal	Annals of Finance
Volume	4
Issue number	1
Early online date	22 Mar 2007
DOIs	https://doi.org/10.1007/s10436-007-0072-4
Publication status	Published - Jan 2008
Externally published	Yes

Bibliographical note

The authors would like to thank Professors Haim Levy, George Wu, Howard E. Thompson, Dietrich K. Fausten, Yew-Kwang Ng and Petko Kalev and the colleagues in University of Wisconsin-Madison, The University of Western Australia, Monash University, The Chinese University of Hong Kong, Hong Kong Baptist University and the University of Technology, Sydney for their valuable comments. The first author would also like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. The research is partially supported by the grants from the Chinese Unversity of Hong Kong and National University of Singapore.

Keywords

Markowitz stochastic dominance
Prospect stochastic dominance
Reverse S-shaped utility function
Risk averse
Risk seeking
S-shaped utility function

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10.1007/s10436-007-0072-4

Cite this

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title = "Prospect and Markowitz stochastic dominance",

abstract = "Levy and Wiener (J Risk Uncertain 16(2), 147-163, 1998), Levy and Lev y (Manage Sci 48(10), 133-1349, 2002; Rev Fin Stud 17(4), 1015-1041, 200 4) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be 'the opposite of' or 'the same as' their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.",

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AB - Levy and Wiener (J Risk Uncertain 16(2), 147-163, 1998), Levy and Lev y (Manage Sci 48(10), 133-1349, 2002; Rev Fin Stud 17(4), 1015-1041, 200 4) develop the prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend their work on prospect stochastic dominance theory (PSD) and Markowitz stochastic dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Furthermore, we formulate the following PSD and MSD properties: hierarchy exists in both PSD and MSD relationships; arbitrage opportunities exist in the first orders of both PSD and MSD; and for any two prospects under certain conditions, their third order MSD preference will be 'the opposite of' or 'the same as' their counterpart third order PSD preference. By extending the work of Levy and Wiener and Levy and Levy, we provide investors with more tools to identify the first and third order PSD and MSD prospects and thus they could make wiser choices on their investment decision.

KW - Markowitz stochastic dominance

KW - Prospect stochastic dominance

KW - Reverse S-shaped utility function

KW - Risk averse

KW - Risk seeking

KW - S-shaped utility function

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DO - 10.1007/s10436-007-0072-4

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SN - 1614-2446

VL - 4

SP - 105

EP - 129

JO - Annals of Finance

JF - Annals of Finance

IS - 1

ER -

Prospect and Markowitz stochastic dominance

Abstract

Bibliographical note

Keywords

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