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MULTIPLICATIVE APPROXIMATION OF WEALTH PROCESSES INVOLVING NO-SHORT-SALES STRATEGIES VIA SIMPLE TRADING

Authors


  • CK would like to thank the warm hospitality of the School of Finance and Economics of the University of Technology Sydney, where the major part of this work was carried out.

Address correspondence to Constantinos Kardaras, Mathematics and Statistics Department, Boston University, 111 Cummington Street, Boston, MA 02215, USA; e-mail: kardaras@bu.edu.

Abstract

A financial market model with general semimartingale asset–price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies.

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