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Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows

Author

Listed:
  • Masaaki Fujii

    (The University of Tokyo)

  • Akihiko Takahashi

    (The University of Tokyo)

Abstract

All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment flows from their clients so that they can avoid the over- as well as under-hedging. In this work, the prices of securities, the occurrences of insured events and (possibly a network of) the investment flows are used to infer their drifts and intensities by a stochastic filtering technique. We utilize the inferred information to provide the optimal hedging strategy based on the mean-variance (or quadratic) risk criterion. A BSDE approach allows a systematic derivation of the optimal strategy, which is shown to be implementable by a set of simple ODEs and the standard Monte Carlo simulation. The presented framework may also be useful for manufactures and energy firms to install an efficient overlay of dynamic hedging by financial derivatives to minimize the costs.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2014. "Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows," CARF F-Series CARF-F-338, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf338
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    References listed on IDEAS

    as
    1. Huyên Pham, 2001. "Mean-Variance Hedging For Partially Observed Drift Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 263-284.
    2. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    3. M. Mania & R. Tevzadze, 2003. "Backward Stochastic PDE and Imperfect Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 663-692.
    4. Kohlmann, Michael & Tang, Shanjian, 2002. "Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 255-288, February.
    5. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," Papers 1306.3359, arXiv.org, revised Nov 2013.
    6. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CARF F-Series CARF-F-332, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market -with supplementary contents for stochastic interest rates-," CIRJE F-Series CIRJE-F-891, CIRJE, Faculty of Economics, University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Papers 1204.2638, arXiv.org, revised Apr 2012.
    9. Masaaki Fujii & Akihiko Takahashi, 2013. "Making Mean-Variance Hedging Implementable in a Partially Observable Market," CARF F-Series CARF-F-321, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Łukasz Delong & Russell Gerrard, 2007. "Mean-variance portfolio selection for a non-life insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 339-367, October.
    11. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
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    Cited by:

    1. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," CIRJE F-Series CIRJE-F-931, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masaaki Fujii, 2016. "A polynomial scheme of asymptotic expansion for backward SDEs and option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 427-445, March.
    3. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," CARF F-Series CARF-F-343, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2014.
    4. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," Papers 1405.0378, arXiv.org, revised Dec 2014.

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