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Approximating Large Diversified Portfolios

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  • Norbert Hofmann
  • Eckhard Platen

Abstract

This 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.

Suggested Citation

  • Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88, January.
    • Handle: RePEc:bla:mathfi:v:10:y:2000:i:1:p:77-88
    DOI: 10.1111/1467-9965.00081
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    Cited by:

    1. Olivier Le Courtois, 2022. "On the Diversification of Fixed Income Assets," Risks, MDPI, vol. 10(2), pages 1-21, February.
    2. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Mirela NICHITA, 2015. "An Overview On State Of Knowledge Of Risk And Risk Management In Economics Fields," SEA - Practical Application of Science, Romanian Foundation for Business Intelligence, Editorial Department, issue 7, pages 423-430, April.
    4. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    5. Herbertsson, Alexander, 2023. "Saddlepoint approximations for credit portfolio distributions with applications in equity risk management," Working Papers in Economics 839, University of Gothenburg, Department of Economics.
    6. 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.
    7. Herbertsson, Alexander, 2023. "Risk management of stock portfolios with jumps at exogenous default events," Working Papers in Economics 836, University of Gothenburg, Department of Economics.
    8. Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.

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