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Structure condition under initial enlargement of filtration

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Abstract

We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period. The structure condition represents essentially an alternative to non-arbitrage conditions for the Markowitz’s portfolio optimization framework, and is crucial for the existence of the optimal portfolio in quadratic utility settings. Herein, we provide practical assumption on the initial market model and the additional information to preserve the structure condition. The stochastic tools that drive this result are a generalization of the Lazaro-Yor representation by Lazaro and Yor (1978) and optional stochastic integral.

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Acknowledgements

The work was supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. G121210818) and National Natural Science Foundation of China (Grant No. 11501105). The authors are grateful to Professor Jia-an Yan and two anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Mathematical and Statistical Sciences Department, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Tahir Choulli

  2. School of Banking and Finance, University of International Business and Economics, Beijing, 100029, China

    Jun Deng

Authors
  1. Tahir Choulli
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  2. Jun Deng
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Correspondence to Tahir Choulli.

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Choulli, T., Deng, J. Structure condition under initial enlargement of filtration. Sci. China Math. 60, 301–316 (2017). https://doi.org/10.1007/s11425-015-0695-4

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  • DOI: https://doi.org/10.1007/s11425-015-0695-4

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