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<p>Portfolio optimization problems have been proposed as a tool for selecting an optimal portfolio for the investors. They assume that the payoff of an investor does not depend on the actions of other investors, ignoring that in many cases a fund manager manages multiple firms’ investments at the same time and the transaction cost incurred by each firm depends on the investments of all the firms due to simultaneous trading from all the accounts. In this paper, we develop a Nash equilibrium based portfolio selection model, in which each firm seeks to maximize its payoff function determined by expected return and transaction cost, and limit the total random loss of a portfolio to a predetermined amount. Because the distributions of random loss vectors are only partially known and are presumed to belong to some uncertainty sets, we express the random loss requirements as distributionally robust chance constraints. We consider various moments based, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>-divergence and Wasserstein distance based uncertainty sets and show that there exists a Nash equilibrium for each uncertainty set. We propose an equivalent mathematical programming problem whose global maximum gives a Nash equilibrium. We perform numerical experiments using actual data from the Indian stock market.</p>

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Distributionally robust chance-constrained game model for portfolio selection in financial market

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Vikas Vikram Singh,
  • Harsha Vardhan Varre

摘要

Portfolio optimization problems have been proposed as a tool for selecting an optimal portfolio for the investors. They assume that the payoff of an investor does not depend on the actions of other investors, ignoring that in many cases a fund manager manages multiple firms’ investments at the same time and the transaction cost incurred by each firm depends on the investments of all the firms due to simultaneous trading from all the accounts. In this paper, we develop a Nash equilibrium based portfolio selection model, in which each firm seeks to maximize its payoff function determined by expected return and transaction cost, and limit the total random loss of a portfolio to a predetermined amount. Because the distributions of random loss vectors are only partially known and are presumed to belong to some uncertainty sets, we express the random loss requirements as distributionally robust chance constraints. We consider various moments based, \(\phi\) -divergence and Wasserstein distance based uncertainty sets and show that there exists a Nash equilibrium for each uncertainty set. We propose an equivalent mathematical programming problem whose global maximum gives a Nash equilibrium. We perform numerical experiments using actual data from the Indian stock market.