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Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance

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  • Guangchen Wang

    (Shandong University)

  • Hua Xiao

    (Shandong University)

Abstract

This paper is concerned with optimal control problems of fully coupled forward–backward stochastic differential equations on finite horizon and infinite horizon with partial information. Two sufficient conditions for optimality are established for the above problems. We demonstrate their applications by four illustrative examples in the framework of cash management, risk minimizing, and linear-quadratic optimal control problems. These examples are explicitly solved based on the sufficient conditions and the optimal filtering of forward–backward stochastic differential equations derived in this paper.

Suggested Citation

  • Guangchen Wang & Hua Xiao, 2015. "Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 639-656, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0625-4
    DOI: 10.1007/s10957-014-0625-4
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    References listed on IDEAS

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    1. Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    2. Antonelli, Fabio & Barucci, Emilio & Mancino, Maria Elvira, 2001. "Asset pricing with a forward-backward stochastic differential utility," Economics Letters, Elsevier, vol. 72(2), pages 151-157, August.
    3. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    4. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    5. Peng, Shige & Shi, Yufeng, 2000. "Infinite horizon forward-backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 75-92, January.
    6. 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. Zhang, Shen & Xu, Juanjuan & Zhang, Huanshui, 2024. "Decentralized control of forward and backward stochastic difference system with nested asymmetric information," Applied Mathematics and Computation, Elsevier, vol. 478(C).

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