Approximating Large Diversified Portfolios
AbstractThis paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one-dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This identifies the asymptotic dynamics of the portfolio as being a lognormal diffusion. Consequentially an efficient way for computing probabilities, derivative prices, and other quantities for the portfolio are obtained. Additionally, the asymptotic strong and weak orders of convergence with respect to the number of assets in the portfolio are determined. Copyright Blackwell Publishers, Inc. 2000.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 10 (2000)
Issue (Month): 1 ()
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627
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- Eckhard Platen, 2004.
"Diversified Portfolios with Jumps in a Benchmark Framework,"
Asia-Pacific Financial Markets,
Springer, vol. 11(1), pages 1-22, March.
- Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
- Truc Le & Eckhard Platen, 2006.
"Approximating the growth optimal portfolio with a diversified world stock index,"
Journal of Risk Finance,
Emerald Group Publishing, vol. 7(5), pages 559-574, November.
- Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
- Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
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