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A Note On Utility Maximization Under Partial Observations1

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  • Ioannis Karatzas
  • Xlng‐Xlong Xue

Abstract

Using ideas from stochastic filtering theory and a martingale representation result of Jacod, we discuss problems of utility maximization in “dynamically incomplete” financial markets under partial observations.

Suggested Citation

  • Ioannis Karatzas & Xlng‐Xlong Xue, 1991. "A Note On Utility Maximization Under Partial Observations1," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 57-70, April.
    • Handle: RePEc:bla:mathfi:v:1:y:1991:i:2:p:57-70
    DOI: 10.1111/j.1467-9965.1991.tb00009.x
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    References listed on IDEAS

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    1. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
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    Cited by:

    1. Dongmei Zhu & Ashley Davey & Harry Zheng, 2025. "S-shaped Utility Maximization with VaR Constraint and Partial Information," Papers 2506.10103, arXiv.org.
    2. Peng, Xingchun & Luo, Liuling, 2025. "Optimal investment strategy for DC pension with mean-weighted variance-CVaR criterion under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 302-324.
    3. Riedel, Frank, 2001. "Existence of Arrow-Radner Equilibrium with Endogenously Complete Markets under Incomplete Information," Journal of Economic Theory, Elsevier, vol. 97(1), pages 109-122, March.
    4. Frank Riedel, 1998. "Imperfect Information Leads to Complete Markets if Dividends are Diffusions," Finance 9808002, University Library of Munich, Germany.
    5. Wolfgang Putschögl & Jörn Sass, 2008. "Optimal consumption and investment under partial information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 137-170, November.
    6. Thomas Lim & Marie-Claire Quenez, 2010. "Portfolio optimization in a default model under full/partial information," Papers 1003.6002, arXiv.org, revised Nov 2013.
    7. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    8. Zongxia Liang & Qi Ye, 2024. "Optimal information acquisition for eliminating estimation risk," Papers 2405.09339, arXiv.org.
    9. Philippe Casgrain & Sebastian Jaimungal, 2018. "Trading algorithms with learning in latent alpha models," Papers 1806.04472, arXiv.org.
    10. Basak, Suleyman, 2000. "A model of dynamic equilibrium asset pricing with heterogeneous beliefs and extraneous risk," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 63-95, January.
    11. Basak, Suleyman, 2005. "Asset pricing with heterogeneous beliefs," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2849-2881, November.
    12. Jérôme Detemple, 1993. "Demande de portefeuille et politique de couverture de risque sous information incomplète," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(1), pages 45-70.
    13. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    14. Detemple, Jerome B., 2002. "Asset pricing in an intertemporal partially-revealing rational expectations equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 219-248, September.
    15. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    16. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    17. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    18. Basak, Suleyman, 2004. "Asset Prices with Heterogenous Beliefs," CEPR Discussion Papers 4256, C.E.P.R. Discussion Papers.
    19. Peng, Xingchun & Hu, Yijun, 2013. "Optimal proportional reinsurance and investment under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 416-428.
    20. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    21. Naik, Narayan Y., 1997. "On aggregation of information in competitive markets: The dynamic case," Journal of Economic Dynamics and Control, Elsevier, vol. 21(7), pages 1199-1227, June.
    22. Naik, Narayan Y., 1997. "Multi-period information markets," Journal of Economic Dynamics and Control, Elsevier, vol. 21(7), pages 1229-1258, June.
    23. Zapatero, Fernando, 1998. "Effects of financial innovations on market volatility when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 597-626, April.
    24. Zhang, Panpan & Yan, Zhiguo, 2024. "Optimal portfolio with relative performance and CRRA risk preferences in a partially observable financial market," Applied Mathematics and Computation, Elsevier, vol. 481(C).

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