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Optimal pricing barriers in a regulated market using reflected diffusion processes

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  • Zheng Han
  • Yaozhong Hu
  • Chihoon Lee

Abstract

We consider a class of one-dimensional (1D) reflected stochastic differential equations (SDEs). Such reflected SDE models arise as the key approximating processes in a regulated financial market system, and our main goal is to determine the set of optimal pricing barriers. We consider the running cost associated with the deviation of the process from the desired target level, and also the control cost from the interventions in an effort to keep the process inside the boundaries. Both a long-time average (ergodic) cost criterion and an infinite horizon discount cost criterion, where the discount factor is allowed to vary from one period to another, are studied, with numerical examples illustrating our main results.

Suggested Citation

  • Zheng Han & Yaozhong Hu & Chihoon Lee, 2016. "Optimal pricing barriers in a regulated market using reflected diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 639-647, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:639-647
    DOI: 10.1080/14697688.2015.1034163
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    References listed on IDEAS

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    1. Lijun Bo & Yongjin Wang & Xuewei Yang, 2010. "Some integral functionals of reflected SDEs and their applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 343-348.
    2. Qin Hu & Yongjin Wang & Xuewei Yang, 2012. "The Hitting Time Density for a Reflected Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 1-18, June.
    3. Budhiraja, Amarjit & Lee, Chihoon, 2007. "Long time asymptotics for constrained diffusions in polyhedral domains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1014-1036, August.
    4. Lijun Bo & Xindan Li & Yongjin Wang & Xuewei Yang, 2013. "On the conditional default probability in a regulated market with jump risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1967-1975, December.
    5. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
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    2. Adams, Daniel & dos Reis, Gonçalo & Ravaille, Romain & Salkeld, William & Tugaut, Julian, 2022. "Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 264-310.

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