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Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations

Published online by Cambridge University Press:  18 June 2009

Nikolai Dokuchaev*
Affiliation:
Department of Mathematics, Trent University, Ontario, Canada. nikolaidokuchaev@trentu.ca Current address: Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Australia. N.Dokuchaev@curtin.edu.au
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Abstract

The paper studies optimal portfolio selection for discrete time market models in mean-variance and goal achieving setting. The optimal strategies are obtained for models with an observed process that causes serial correlations of price changes. The optimal strategies are found to be myopic for the goal-achieving problem and quasi-myopic for the mean variance portfolio.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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References

N.G. Dokuchaev, Dynamic portfolio strategies: quantitative methods and empirical rules for incomplete information. Kluwer, Boston (2002).
Dokuchaev, N., Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. IMA J. Management Mathematics 17 (2006) 257276. CrossRef
Dokuchaev, N., Discrete time market with serial correlations and optimal myopic strategies. European J. Oper. Res. 177 (2007) 10901104. CrossRef
Dokuchaev, N., Maximin investment problems for discounted and total wealth. IMA J. Management Mathematics 19 (2008) 6374. CrossRef
N Dokuchaev, Optimality of myopic strategies for multi-stock discrete time market with management costs. European J. Oper. Res. (to appear).
Dokuchaev, N.G. and Haussmann, U., Optimal portfolio selection and compression in an incomplete market. Quantitative Finance 1 (2001) 336345. CrossRef
Dynkin, E. and Evstigneev, I., Regular conditional expectations of correspondences. Theory Probab. Appl. 21 (1976) 325338. CrossRef
Feldman, D., Incomplete information equilibria: separation theorem and other myths. Ann. Oper. Res. 151 (2007) 119149. CrossRef
Hakansson, N.H., On optimal myopic portfolio policies, with and without serial correlation of yields. J. Bus. 44 (1971) 324334. CrossRef
P. Henrotte, Dynamic mean variance analysis. Working paper, SSRN: http://ssrn.com/abstract=323397 (2002).
C. Hipp and M. Taksar, Hedging general claims and optimal control. Working paper (2000).
H. Leland, Dynamic Portfolio Theory. Ph.D. Thesis, Harvard University, USA (1968).
Li, D. and Optimal, W.L. Ng portfolio selection: multi-period mean-variance optimization. Math. Finance 10 (2000) 387406. CrossRef
Lim, A., Quadratic hedging and mean-variance portfolio selection with random parameters in an incomplete market. Math. Oper. Res. 29 (2004) 132161. CrossRef
Lim, A. and Zhou, X.Y., Mean-variance portfolio selection with random parameters in a complete market. Math. Oper. Res. 27 (2002) 101120. CrossRef
D.G. Luenberger, Optimization by Vector Space Methods. John Wiley, New York (1968).
H.M. Markowitz, Portfolio Selection: Efficient Diversification of Investment. New York: John Wiley & Sons (1959).
Merton, R., Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Economics Statistics 51 (1969) 247257. CrossRef
Mossin, J., Optimal multi-period portfolio policies. J. Business 41 (1968) 215229. CrossRef
S.R. Pliska, Introduction to mathematical finance: discrete time models. Blackwell Publishers (1997).
Schweizer, M., Variance-optimal hedging in discrete time. Math. Oper. Res. 20 (1995) 132. CrossRef