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Mean reflected stochastic differential equations with two constraints

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  • Falkowski, Adrian
  • Słomiński, Leszek

Abstract

We study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some functionals depending on the law of the solution lie between two given càdlàg constraints. Applications to investment models with constraints are given.

Suggested Citation

  • Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
    • Handle: RePEc:eee:spapps:v:141:y:2021:i:c:p:172-196
    DOI: 10.1016/j.spa.2021.07.008
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    References listed on IDEAS

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    1. Slominski, Leszek & Wojciechowski, Tomasz, 2010. "Stochastic differential equations with jump reflection at time-dependent barriers," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1701-1721, August.
    2. Philippe Briand & Romuald Elie & Ying Hu, 2018. "BSDEs with mean reflection," Post-Print hal-01318649, HAL.
    3. Falkowski, Adrian & Słomiński, Leszek, 2017. "SDEs with constraints driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3536-3557.
    4. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
    5. Nicole Bäuerle & Ulrich Rieder, 2013. "Optimal Deterministic Investment Strategies for Insurers," Risks, MDPI, vol. 1(3), pages 1-18, November.
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