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<p>In this study, we analyze the saddle point of the mean-field stochastic mixed delay differential system with Teugels martingales over an infinitely long time horizon. In addition to this, the mean-field term is generalized to the Fr<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\acute{e}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>e</mi> <mo>´</mo> </mover> </math></EquationSource> </InlineEquation>chet differentiable functional. Moreover, when the control domain is convex, the transversality condition is employed to establish the essential criteria for optimality, including the stochastic maximum principle (saddle point) and necessary conditions for optimality. Finally, the optimal irreversible investment problem is demonstrated with the help of the aforementioned theoretical work.</p>

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Optimal Stochastic Singular Control for Mixed Delay Differential Game with Brownian Noise and Teugels Martingales

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • R. Deepa,
  • G. Saranya,
  • P. Muthukumar,
  • Mokhtar Hafayed

摘要

In this study, we analyze the saddle point of the mean-field stochastic mixed delay differential system with Teugels martingales over an infinitely long time horizon. In addition to this, the mean-field term is generalized to the Fr \(\acute{e}\) e ´ chet differentiable functional. Moreover, when the control domain is convex, the transversality condition is employed to establish the essential criteria for optimality, including the stochastic maximum principle (saddle point) and necessary conditions for optimality. Finally, the optimal irreversible investment problem is demonstrated with the help of the aforementioned theoretical work.