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Partially Observed Time-Inconsistency Recursive Optimization Problem and Application

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  • Haiyang Wang

    (Shandong University)

  • Zhen Wu

    (Shandong University)

Abstract

In this paper, we study a partially observed recursive optimization problem, which is time inconsistent in the sense that it does not admit the Bellman optimality principle. To obtain the desired results, we establish the Kalman–Bucy filtering equations for a family of parameterized forward and backward stochastic differential equations, which is a Hamiltonian system derived from the general maximum principle for the fully observed time-inconsistency recursive optimization problem. By means of the backward separation technique, the equilibrium control for the partially observed time-inconsistency recursive optimization problem is obtained, which is a feedback of the state filtering estimation. To illustrate the applications of theoretical results, an insurance premium policy problem under partial information is presented, and the observable equilibrium policy is derived explicitly.

Suggested Citation

  • Haiyang Wang & Zhen Wu, 2014. "Partially Observed Time-Inconsistency Recursive Optimization Problem and Application," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 664-687, May.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:2:d:10.1007_s10957-013-0326-4
    DOI: 10.1007/s10957-013-0326-4
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    1. Norberg, Ragnar, 1999. "Ruin problems with assets and liabilities of diffusion type," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 255-269, June.
    2. Steven M. Goldman, 1980. "Consistent Plans," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 533-537.
    3. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
    4. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    5. Boswijk, H. Peter & Hommes, Cars H. & Manzan, Sebastiano, 2007. "Behavioral heterogeneity in stock prices," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1938-1970, June.
    6. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2011. "Time-Inconsistent Stochastic Linear--Quadratic Control," Papers 1111.0818, arXiv.org.
    7. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    8. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    9. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    10. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    11. Nicolas Vieille & Jörgen Weibull, 2009. "Multiple solutions under quasi-exponential discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 513-526, June.
    12. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    13. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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    Cited by:

    1. Haiyang Wang & Ruimin Xu, 2023. "Time-Inconsistent LQ Games for Large-Population Systems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1249-1268, June.

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