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Mean-field equilibrium price formation under single-default risk

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  • Masashi Sekine

Abstract

We study equilibrium price formation in an incomplete financial market with a large population of agents, where stock prices are subject to a single-default event. Agents are assumed to be heterogeneous in their risk aversion and terminal liabilities, and maximize exponential utility of terminal net wealth. We first characterize each agent's optimal strategy by a quadratic-growth backward stochastic differential equation (BSDE) driven by Brownian motions and a compensated default martingale. We then formulate the market-clearing condition in terms of aggregate optimal demand and derive a mean-field quadratic-growth BSDE for the equilibrium risk premium. The resulting characterization quantifies how default intensity, jump size, and agent heterogeneity jointly shape the default-risk component of equilibrium security risk premia. Under a Markovian factor model, we establish short-time solvability of the mean-field BSDE through a fixed-point argument based on estimates for a coupled semilinear PDE system. Finally, we show that the risk premium characterized by the mean-field BSDE asymptotically clears the market as the population size tends to infinity.

Suggested Citation

  • Masashi Sekine, 2026. "Mean-field equilibrium price formation under single-default risk," Papers 2607.17502, arXiv.org.
    • Handle: RePEc:arx:papers:2607.17502
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    References listed on IDEAS

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    1. Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.
    2. Masashi Sekine, 2026. "Mean Field Equilibrium Asset Pricing Models With Exponential Utility," Papers 2603.22058, arXiv.org.
    3. Masaaki Fujii & Masashi Sekine, 2026. "Mean Field Equilibrium Asset Pricing Model with Habit Formation," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 33(1), pages 263-314, March.
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    5. Masaaki Fujii, 2022. "Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations," Papers 2209.12639, arXiv.org, revised Jun 2023.
    6. Masashi Sekine, 2024. "Mean field equilibrium asset pricing model under partial observation: An exponential quadratic Gaussian approach," Papers 2410.01352, arXiv.org, revised Apr 2025.
    7. Monique Jeanblanc & Marc Yor & Marc Chesney, 2009. "Mathematical Methods for Financial Markets," Springer Finance, Springer, number 978-1-84628-737-4, February.
    8. Masaaki Fujii, 2025. "Mean-Field Price Formation on Trees with a Network of Relative Performance Concerns," Papers 2512.21621, arXiv.org.
    9. Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    10. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
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