A Multi-objective Approach to Multi-period: Portfolio Optimization with Transaction Costs
- 483 Downloads
Portfolio optimization with transaction costs is a problem that involves non-smooth functions.
Transaction costs on each asset are usually assumed to be convex functions of the amount sold or bought. These functions can be non-differentiable in a finite number of points. In this chapter we intend to extend Markowitz’s portfolio selection model to multi-period models which include proportional transaction costs in the presence of initial holdings for the investor. Our approach is a novel one. We do research on an investor issue applicable to a business person who has some initial holdings and knows within the envisaged time frame the outbound and inbound cash flows as well as the exact points in time when these financial flows will occur.
A multi-period portfolio selection problem as a multi-objective programming problem with complementarity constraints is formulated. We prove that the above model is equivalent with a mixed-binary model. A goal programming approach to the multi-period multi-objective problem for portfolio selection is studied. In order to include the investor’s preferences, satisfaction functions are considered.
KeywordsPortfolio optimization Multi-objective Multi-period Transaction costs Complementarity constraints
This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0908.
- Aouni, B., Colapinto, C., & La Torre, D., Liuzzi, D., & Marsiglio, S. (2015). On dynamic multiple criteria decision making models: A goal programming approach. In M. Al-Shammari & H. Masri (Eds.), Multiple criteria decision making in finance, insurance and investment, multiple criteria decision making (pp. 31–48). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-21158-9_3
- Atta Mills, E. F. E., Yan, D., Yu, B., & Wei, X. (2016). Research on regularized mean–variance portfolio selection strategy with modified Roy safety-first principle. SpringerPlus, 5(919), 1–18.Google Scholar
- Brodt, A. I. (1979). A multi-period portfolio theory model for commercial bank management. In E. Elton & M. J. Gruber (Eds.), Portfolio theory, TIMS studies in the management sciences (pp. 191–213). Amsterdam: North Holland.Google Scholar
- Brodt, A. I. (1984). Intertemporal bank asset and liability management. Journal of Bank Research, 15, 82–94.Google Scholar
- Chapados, N. (2011). Multiperiod problems, Chapter 3. In Portfolio choice problems: An introductory survey of single and multiperiod models. SpringerBriefs in electrical and computer engineering (Vol. 3, pp. 37–59). New York: Springer.Google Scholar
- Colapinto, C., & La Torre, D. (2015). Multiple criteria decision making and goal programming for optimal venture capital investments and portfolio management. In M. Al-Shammari & H. Masri (Eds.), Multiple criteria decision making in finance, insurance and investment, multiple criteria decision making (pp. 9–30). Cham: Springer International Publishing. doi https://doi.org/10.1007/978-3-319-21158-9_2.
- Dempster, M. A. H., & Ireland, A. M. (1988). A financial expert decision support system. In G. Mitra (Ed.), Mathematical models for decision support. NATO ASI Series (Vol. F48, pp. 415–440). Berlin: Springer.Google Scholar
- Fama, E. (1970). Multi-period consumption-investment decision. American Economic Review, 60, 163–179.Google Scholar
- Frauendorfer, K., & Siede, H. (1999). Portfolio selection using multistage stochastic programming. Central European Journal of Operations Research, 7(4), 277–289.Google Scholar
- Fu, Y. H., Ng, K. M., Huang, B., & Huang, H. C. (2015). Portfolio optimization with transaction costs: A two-period mean-variance model. Annals of Operations Research, 233–135.Google Scholar
- Hakansson, N. H. (1979). Optimal multi-period portfolio policies. In E. Elton & M. J. Gruber (Eds.), Portfolio theory, TIMS studies in the management sciences (p. 11). Amsterdam: North Holland.Google Scholar
- Lane, M., & Hutchinson, P. (1980). A model for managing a certificate of deposit portfolio under uncertainty. In M. A. H. Dempster (Eds.), Stochastic programming (pp. 473–495). London: Academic Press.Google Scholar
- Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.Google Scholar
- Markowitz, H. M. (1959). Portfolio selection: Efficient diversification of investments. New York: Wiley.Google Scholar
- Markowitz, H. M. (1987). Mean-variance analysis in portfolio choice and capital markets. Cambridge, MA: Basil Blackwell Ltd.Google Scholar
- Mossin, J. (1968). Optimal multi-period portfolio policies. Journal of Bussiness, 41, 215–229.Google Scholar
- Peng, Z., & Jin, P. (2012). The optimization on the multiperiod mean average absolute deviation fuzzy portfolio selection. In: D. Jin & S. Lin (Eds.), Advances in electronic engineering, communication and management vol.2. Lecture notes in electrical engineering (Vol. 140). Berlin: Springer.Google Scholar
- Pogue, G. A. (1970). An extension of the Markowitz portfolio selection model to include transaction costs, short sales, leverage policies and taxes. Journal of Finance, 25, 1005–1027.Google Scholar
- Radulescu, M., Radulescu, S., & Radulescu, C. Z. (2001). Computer simulation for portfolio selection models with transaction costs and initial holdings. In Proceedings of the EUROSIM 2001 Congress, “Shaping future with simulation”, Delft, pp. 1–6.Google Scholar
- Radulescu, C-Z, Radulescu, M., & Radulescu, S. (2002). Optimal decisions for portfolio selection in the presence of initial holdings and transaction costs. In Proceeding of the 4th International Workshop on Computer Science and Information Technologies CSIT’2002, Patras, pp. 1–6.Google Scholar
- Shapiro, J. F. (1988). Stochastic programming models for dedicated portfolio selection. In: B. Mitra (Ed.), Mathematical models for decision support. NATO ASI Series (Vol. F48, pp. 587–611). Berlin: Springer.Google Scholar
- Wang, S., & Xia, Y. (2002). Portfolio selection and asset pricing. New York: Springer.Google Scholar
- Zhang, W. G., Liu, Y. J., & Xu, W. J. (2012). A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs. European Journal of Operational Research, 222(2), 341–349.Google Scholar
- Zhang, P., & Yu, L. (2011). The optimization on the multiperiod mean-VaR portfolio selection in friction market. In: D. Jin & S. Lin (Eds.), Advances in multimedia, software engineering and computing vol. 2. Advances in Intelligent and Soft Computing (Vol. 129). Berlin: Springer.Google Scholar