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A robust investment-consumption optimization problem in a switching regime interest rate setting

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  • Bogdan Iftimie

    (Bucharest University of Economic Studies)

Abstract

In this paper we are dealing with a robust investment-consumption optimization problem in an incomplete market with a switching regime stochastic interest rate. Our methodology combines duality approach with stochastic control techniques (applied to the dual problem) specific to a non-Markovian setting, such as dynamic programming principle (initiated in Karoui and Quenez (SIAM J Control Optim 33(1):29–66, 1995)) and Backward Stochastic Differential Equations (BSDEs) theory. An auxiliary dual problem is established by means of infinite-dimensional convex duality. We derive explicit formulas for the optimal trading strategy and consumption rate in terms of the solution of some nonstandard BSDE with jumps. Links to other significant results in the domain are also provided.

Suggested Citation

  • Bogdan Iftimie, 2023. "A robust investment-consumption optimization problem in a switching regime interest rate setting," Journal of Global Optimization, Springer, vol. 86(3), pages 713-739, July.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:3:d:10.1007_s10898-023-01273-0
    DOI: 10.1007/s10898-023-01273-0
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    References listed on IDEAS

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    1. Jeanblanc, Monique & Song, Shiqi, 2015. "Martingale representation property in progressively enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4242-4271.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    3. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    4. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    5. Anne Gundel, 2005. "Robust utility maximization for complete and incomplete market models," Finance and Stochastics, Springer, vol. 9(2), pages 151-176, April.
    6. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    7. Ariel Neufeld & Marcel Nutz, 2018. "Robust Utility Maximization With Lã‰Vy Processes," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 82-105, January.
    8. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 1-20, February.
    9. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    10. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
    11. Jeanblanc, Monique & Le Cam, Yann, 2009. "Progressive enlargement of filtrations with initial times," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2523-2543, August.
    12. Pham, Huyên, 2010. "Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1795-1820, August.
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