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Uniqueness and Existence of Linear Equilibrium with a Constrained Trader

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  • Heeyoung Kwon
  • Jin Hyuk Choi

Abstract

We study a discrete-time financial market with a single constrained trader, competitive market makers, and noise traders. Within the class of linear equilibria, the equilibrium structure is shown to be uniquely determined by two state variables: the market maker's expectation of the trader's remaining demand and the residual demand beyond this expectation. This discrete-time uniqueness result aligns with its continuous-time analogue, indicating that the latter may emerge as the unique limit within the same class. We also prove the existence of a linear equilibrium, providing formal support to numerical and empirical findings in related work.

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  • Heeyoung Kwon & Jin Hyuk Choi, 2025. "Uniqueness and Existence of Linear Equilibrium with a Constrained Trader," Papers 2508.10138, arXiv.org.
    • Handle: RePEc:arx:papers:2508.10138
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    File URL: http://arxiv.org/pdf/2508.10138
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