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Diagonally quadratic BSDE with oblique reflection and optimal switching

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  • Luo, Peng
  • Zhu, Mengbo

Abstract

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence of a solution by providing some delicate a priori estimates. We further obtain the uniqueness by verifying the first component of the solution is indeed the value of a switching problem for quadratic BSDEs. Moreover, we provide an extension for the solvability and apply our results to study a risk-sensitive switching problem for functional stochastic differential equations.

Suggested Citation

  • Luo, Peng & Zhu, Mengbo, 2024. "Diagonally quadratic BSDE with oblique reflection and optimal switching," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001303
    DOI: 10.1016/j.spa.2024.104424
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    References listed on IDEAS

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    1. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
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    6. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    7. Bénézet, Cyril & Chassagneux, Jean-François & Richou, Adrien, 2022. "Switching problems with controlled randomisation and associated obliquely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 23-71.
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