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Robust Portfolio Choice and Indifference Valuation

Author

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  • Roger J. A. Laeven

    () (Department of Quantitative Economics, University of Amsterdam, EURANDOM and CentER, 1018 XE Amsterdam, The Netherlands)

  • Mitja Stadje

    () (Department of Econometrics and Operations Research, Tilburg University and CentER, 5000 LE Tilburg, The Netherlands)

Abstract

We solve, theoretically and numerically, the problems of optimal portfolio choice and indifference valuation in a general continuous-time setting. The setting features (i) ambiguity and time-consistent ambiguity-averse preferences, (ii) discontinuities in the asset price processes, with a general and possibly infinite activity jump part next to a continuous diffusion part, and (iii) general and possibly nonconvex trading constraints. We characterize our solutions as solutions to backward stochastic differential equations (BSDEs). Generalizing Kobylanski's result for quadratic BSDEs to an infinite activity jump setting, we prove existence and uniqueness of the solution to a general class of BSDEs, encompassing the solutions to our portfolio choice and valuation problems as special cases. We provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium, and a further decomposition into a piece stemming from the diffusion part and a piece stemming from the jump part. We further compute our solutions in a few examples by numerically solving the corresponding BSDEs using regression techniques.

Suggested Citation

  • Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
  • Handle: RePEc:inm:ormoor:v:39:y:2014:i:4:p:1109-1141
    DOI: 10.1287/moor.2014.0646
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    File URL: http://dx.doi.org/10.1287/moor.2014.0646
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta hedging in a jump-diffusion model," Papers 1910.08946, arXiv.org.
    2. Power, Gabriel J. & Eaves, James & Turvey, Calum & Vedenov, Dmitry, 2017. "Catching the curl: Wavelet thresholding improves forward curve modelling," Economic Modelling, Elsevier, vol. 64(C), pages 312-321.
    3. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    4. Wong, K.C. & Yam, S.C.P. & Zeng, J., 2019. "Mean-risk portfolio management with bankruptcy prohibition," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 153-172.
    5. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    6. Kerem Ugurlu, 2018. "Portfolio Optimization with Nondominated Priors and Unbounded Parameters," Papers 1807.05773, arXiv.org.
    7. Wahid Faidi & Anis Matoussi & Mohamed Mnif, 2017. "Optimal Stochastic Control Problem Under Model Uncertainty With Nonentropy Penalty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-41, May.
    8. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    9. Alessandro Calvia & Emanuela Rosazza Gianin, 2019. "Risk measures and progressive enlargement of filtration: a BSDE approach," Papers 1904.13257, arXiv.org, revised Mar 2020.
    10. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.
    11. D. Madan & M. Pistorius & M. Stadje, 2017. "On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation," Finance and Stochastics, Springer, vol. 21(4), pages 1073-1102, October.
    12. Delong, Łukasz & Dhaene, Jan & Barigou, Karim, 2019. "Fair valuation of insurance liability cash-flow streams in continuous time: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 196-208.

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