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<p>This paper focuses on a kind of McKean-Vlasov backward stochastic differential equation with Markov regime switching, while the terminal state is constrained in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}_{+}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">R</mi> <mo>+</mo> </msub> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> By virtue of the terminal perturbation method developed by Ji and Peng [<CitationRef CitationID="CR7">7</CitationRef>] and Ekeland’s variational principle, we establish a stochastic maximum principle (necessary condition) for the optimal terminal state under Lions derivative. As an application, we explore the backward formulation of continuous-time mean-variance portfolio selection with bankruptcy prohibition under two market regimes (bull market and bear one) and derive the corresponding optimal terminal wealth as well.</p>

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Terminal perturbation for McKean-Vlasov BSDE with regime switching and application to finance

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Binyan Mei,
  • Liangquan Zhang

摘要

This paper focuses on a kind of McKean-Vlasov backward stochastic differential equation with Markov regime switching, while the terminal state is constrained in \(\mathbb {R}_{+}.\) R + . By virtue of the terminal perturbation method developed by Ji and Peng [7] and Ekeland’s variational principle, we establish a stochastic maximum principle (necessary condition) for the optimal terminal state under Lions derivative. As an application, we explore the backward formulation of continuous-time mean-variance portfolio selection with bankruptcy prohibition under two market regimes (bull market and bear one) and derive the corresponding optimal terminal wealth as well.