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<p>We study the existence of equilibrium in dynamic asset markets where agents possess quasi-concave mean-value utility functions. These markets extend the classical Arrow–Debreu framework to the case where consumption sets are unbounded from below and continuous trading occurs over a finite time interval. The dynamic asset market problem is reformulated as a quasi-variational inequality (QVI) with unbounded constraint maps, and sufficient conditions for the existence of solutions to this class of QVI problems are established. The QVI formulation subsequently ensures the existence of equilibrium for the given economic model under a coercivity condition, without relying on traditional no-arbitrage assumptions. Finally, we propose an algorithm for computing an equilibrium of dynamic asset markets by resolving the corresponding quasi-variational inequality into variational inequalities.</p>

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Existence results and computational methods for dynamic asset markets through quasi-variational inequalities

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Shivani Valecha,
  • Asrifa Sultana

摘要

We study the existence of equilibrium in dynamic asset markets where agents possess quasi-concave mean-value utility functions. These markets extend the classical Arrow–Debreu framework to the case where consumption sets are unbounded from below and continuous trading occurs over a finite time interval. The dynamic asset market problem is reformulated as a quasi-variational inequality (QVI) with unbounded constraint maps, and sufficient conditions for the existence of solutions to this class of QVI problems are established. The QVI formulation subsequently ensures the existence of equilibrium for the given economic model under a coercivity condition, without relying on traditional no-arbitrage assumptions. Finally, we propose an algorithm for computing an equilibrium of dynamic asset markets by resolving the corresponding quasi-variational inequality into variational inequalities.