Document Type : Research Article
Authors
1 Department of mathematics,Faculty of Mathematics and Computer Science, Allameh Tabataba‘i University, Tehran, Iran.
2 Department of Mathematics, Allameh Tabatabai University, Tehran, Iran
Abstract
The portfolio optimization problem, including portfolio selection, typically aims to maximize return and minimize risk. In this paper, we discuss about increasing use of stochastic portfolios in investments and aim to create optimal portfolios. It follows the relative wealth process of these portfolios, outperforms the market portfolio over sufficiently long time-horizons. In this regard, initially, a model of the market is presented by the stochastic portfolio theory (SPT) and features like Growth rate, Excess growth rate are mentioned. Then, functionally-generated portfolios are defined by using diversity weighted portfolios with parameters p ∈ (0, 1), p < 0 and combination of them. Finally, by obtaining the daily closing price of 10 stocks in Tehran Stock Exchange (TSE) ,the performance of diversity weighted portfolios is investigated.
Keywords
[2] R. Fernholz, On the diversity of equity markets, Journal of Mathematical Economics, 31(3)
(1999a), 393–417.
[3] R. Fernholz, I. Shay, Stochastic Portfolio Theory and Stock Market Equilibrium, 1982.
[4] E. R. Fernholz, I. Karatzas, Stochastic Portfolio Theory: an Overview, 2008.
[5] R. Fernholz, I. Karatzas, Stochastic Portfolio Theory: a survey, in: A. Bensoussan, Q.
Zhang (eds), Handbook of Numerical Analysis, Vol. XV, Special Volume: Mathematical
Modeling and Numerical Methods in Finance, Volume 15 of Handbook of Numerical Analysis,
Amsterdam: Elsevier/North-Holland, 2009.
[6] R. Fernholz, I. Karatzas, C. Kardaras, Diversity and relative arbitrage in equity markets,
Finance Stoch, 9(1) (2005), 1–27.
[7] I. Karatzas, Lectures on the Mathematics of Finance, Providence, RI: American Mathematical Society, 1997.
[8] I. Karatzas, S. Shreve, Methods of Mathematical Finance, New York: Springer-Verlag,
1998.
[9] C. Kardaras, Stochastic portfolio theory in semimartingale markets, Preprint, Columbia
University, 2004.
[10] D. Kim, Market-to-book ratio in stochastic portfolio theory, Finance and Stochastics, 27
(2023), 401434.
[11] H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77–91.
[12] W. F. Sharpe, Mutual Fund Performance, Journal of Business, 39 (S1) (1966), 119–138.
[13] A. Vervuurt, I. Karatzas, Diversity-weighted portfolios with negative parameter, SpringerVerlag Berlin Heidelberg, 2015.
)