A simple SSD-efficiency test
Tóm tắt
A linear programming SSD-efficiency test capable of identifying a dominating portfolio is proposed. It has
$$T+n$$
variables and at most
$$2T+1$$
constraints, whereas the existing SSD-efficiency tests are either unable to identify a dominating portfolio, or require solving a linear program with at least
$$O(T^2+n)$$
variables and/or constraints.
Tài liệu tham khảo
Dentcheva, D., Ruszczyński, A.: Optimization with stochastic dominance constraints. SIAM J. Optim. 14(2), 548–566 (2003)
Dentcheva, D., Ruszczyński, A.: Portfolio optimization with stochastic dominance constraints. J. Banking Finance 30(2), 433–451 (2006)
Fabian, C.I., Mitra, G., Roman, D.: Second-order stochastic dominance models using cutting-plane representations. Math. Program. 130, 33–57 (2011)
Föllmer, H., Schied, A.: Stochastic Finance, 2nd edn. de Gruyter, Berlin (2004)
Grechuk, B., Molyboha, A., Zabarankin, M.: Mean-deviation analysis in the theory of choice. Risk Anal. 32(8), 1277–1292 (2012)
Grechuk, B., Zabarankin, M.: Inverse portfolio problem with mean-deviation model. European J. Oper. Res. 234(2), 481–490 (2014)
Hadar, J., Russell, W.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59, 25–34 (1969)
Kopa, M., Chovanec, P.: A second-order stochastic dominance portfolio efficiency measure. Kybernetika 44(2), 243–258 (2008)
Kopa, M., Post, T.: A general test for portfolio efficiency. Working paper (2011). http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1824174
Kuosmanen, T.: Efficient diversification according to stochastic dominance criteria. Manage. Sci. 50(10), 1390–1406 (2004)
Levy, H.: Stochastic dominance and expected utility: survey and analysis. Manage. Sci. 38(4), 555–593 (1992)
Luedtke, J.: New formulations for optimization under stochastic dominance constraints. SIAM J. Optim. 19, 1433–1450 (2008)
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, 3rd edn. Princeton University Press, Princeton (1953)
Ng, M.C.: A remark on third degree stochastic dominance. Manage. Sci. 46(6), 870–873 (2000)
Post, T.: Empirical tests for stochastic dominance efficiency. J. Finance 58, 1905–1932 (2003)
Post, T.: On the dual test for SSD efficiency with an application to momentum investment strategies. Eur. J. Oper. Res. 185, 1564–1573 (2008)
Post, T., Kopa, M.: General linear formulations of stochastic dominance criteria. Eur. J. Oper. Res. 230, 321–332 (2013)
Rothschild, M., Stiglitz, J.: Increasing risk I: a definition. J. Econ. Theory 2(3), 225–243 (1970)
Yaari, M.E.: The dual theory of choice under risk. Econometrica 55, 95–115 (1987)