TY - JOUR
T1 - Prospect and Markowitz stochastic dominance
AU - Wong, W. -K.
AU - Chan, R. H.
N1 - Funding Information:
Acknowledgments 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.
PY - 2008/1
Y1 - 2008/1
N2 - 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.
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 - Prospect stochastic dominance
KW - Markowitz stochastic dominance
KW - Risk seeking
KW - Risk averse
KW - S-shaped utility function
KW - Reverse S-shaped utility function
UR - http://www.scopus.com/inward/record.url?scp=36348949227&partnerID=8YFLogxK
U2 - 10.1007/s10436-007-0072-4
DO - 10.1007/s10436-007-0072-4
M3 - Journal article
AN - SCOPUS:36348949227
SN - 1614-2446
VL - 4
SP - 105
EP - 129
JO - Annals of Finance
JF - Annals of Finance
IS - 1
ER -