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Dynamic credit investment in partially observed markets

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  • Agostino Capponi
  • José Figueroa-López
  • Andrea Pascucci

Abstract

We consider the problem of maximizing the expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous-time finite-state Markov chain. We reduce the partially observed stochastic control problem to a complete observation risk-sensitive control problem via the filtered regime switching probabilities. We separate the latter into predefault and postdefault dynamic optimization subproblems and obtain two coupled Hamilton–Jacobi–Bellman (HJB) partial differential equations. We prove the existence and uniqueness of a globally bounded classical solution to each HJB equation and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high-growth regimes increases, and decreases his credit risk exposure as the filter probability of being in high default risk regimes gets larger. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Agostino Capponi & José Figueroa-López & Andrea Pascucci, 2015. "Dynamic credit investment in partially observed markets," Finance and Stochastics, Springer, vol. 19(4), pages 891-939, October.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:4:p:891-939
    DOI: 10.1007/s00780-015-0272-0
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    Cited by:

    1. Xie, Lin & Chen, Lv & Qian, Linyi & Li, Danping & Yang, Zhixin, 2023. "Optimal investment and consumption strategies for pooled annuity with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 129-155.
    2. John R. Birge & Lijun Bo & Agostino Capponi, 2018. "Risk-Sensitive Asset Management and Cascading Defaults," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 1-28, February.
    3. Lijun Bo & Huafu Liao & Xiang Yu, 2017. "Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching," Papers 1712.05676, arXiv.org, revised Oct 2018.
    4. Christoph Belak & Sören Christensen & Olaf Menkens, 2016. "Worst-Case Portfolio Optimization In A Market With Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-36, March.
    5. Oliver Janke, 2016. "Utility Maximization and Indifference Value under Risk and Information Constraints for a Market with a Change Point," Papers 1610.08644, arXiv.org.
    6. Lijun Bo & Agostino Capponi, 2016. "Optimal Investment under Information Driven Contagious Distress," Papers 1612.06133, arXiv.org.
    7. Justin A. Sirignano & Gerry Tsoukalas & Kay Giesecke, 2016. "Large-Scale Loan Portfolio Selection," Operations Research, INFORMS, vol. 64(6), pages 1239-1255, December.
    8. Lijun Bo & Agostino Capponi, 2017. "Optimal Credit Investment with Borrowing Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 546-575, May.
    9. Lijun Bo & Agostino Capponi, 2017. "Robust Optimization of Credit Portfolios," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 30-56, January.

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    More about this item

    Keywords

    Partial information; Filtering; Risk-sensitive control; Default risk; Hidden Markov chain; 93E20; 91G10; 49L20; 93E11; G11; C61; C11;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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