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Optimal Consumption And Portfolio Decisions With Partially Observed Real Prices

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  • Alain Bensoussan
  • Jussi Keppo
  • Suresh P. Sethi

Abstract

We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the basket price and (ii) when he receives only noisy observations on the basket price. We derive the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases. The compositions of the funds in the two cases are the same, but in general the investor's allocations of his wealth into these funds will differ. However, in the particular case when the investor has constant relative risk‐aversion (CRRA) utility, his optimal investment allocations into these funds are also the same in both cases.

Suggested Citation

  • Alain Bensoussan & Jussi Keppo & Suresh P. Sethi, 2009. "Optimal Consumption And Portfolio Decisions With Partially Observed Real Prices," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 215-236, April.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:2:p:215-236
    DOI: 10.1111/j.1467-9965.2009.00362.x
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    Cited by:

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    2. Claus Munk & Alexey Rubtsov, 2014. "Portfolio management with stochastic interest rates and inflation ambiguity," Annals of Finance, Springer, vol. 10(3), pages 419-455, August.
    3. Zhang, Ling & Zhang, Hao & Yao, Haixiang, 2018. "Optimal investment management for a defined contribution pension fund under imperfect information," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 210-224.
    4. Guohui Guan, 2020. "Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 25-47, March.
    5. repec:dau:papers:123456789/7471 is not listed on IDEAS
    6. Sangmin Lee & Andrew Papanicolaou, 2016. "Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-36, December.
    7. Mondher Bellalah & Detao Zhang & Panpan Zhang, 2023. "An optimal portfolio and consumption problem with a benchmark and partial information," Mathematics and Financial Economics, Springer, volume 17, number 6, February.
    8. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    9. Michael Jong Kim, 2020. "Variance Regularization in Sequential Bayesian Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 966-992, August.
    10. Dai, Min & Huang, Shan & Keppo, Jussi, 2019. "Opaque bank assets and optimal equity capital," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 369-394.
    11. Chevalier-Roignant, Benoît & Flath, Christoph M. & Kort, Peter M. & Trigeorgis, Lenos, 2021. "Capacity investment choices under cost heterogeneity and output flexibility in oligopoly," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1154-1173.
    12. Weiyin Fei, 2014. "Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisions," Papers 1401.2531, arXiv.org.
    13. Y, Ivanenko. & B, Munier., 2012. "Price as a choice under nonstochastic randomness in finance," Working papers 381, Banque de France.
    14. 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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