AI 中文总结
研究不完全金融市场中单一违约风险下的均衡价格形成，通过二次增长倒向随机微分方程刻画参与者最优策略，推导出均值场二次增长BSDE，量化相关因素对风险溢价的影响，建立短时可解性并证明风险溢价渐近使市场出清。
AI 中文摘要
我们研究了一个不完全金融市场中的均衡价格形成，其中有大量的参与者，股票价格受到单一违约事件的影响。假设参与者在风险厌恶和终端负债方面存在异质性，并最大化终端净财富的指数效用。我们首先通过由布朗运动和补偿违约鞅驱动的二次增长倒向随机微分方程（BSDE）来刻画每个参与者的最优策略。然后，我们根据总最优需求来制定市场出清条件，并推导出用于均衡风险溢价的均值场二次增长BSDE。所得的刻画量化了违约强度、跳跃大小和参与者异质性如何共同塑造均衡证券风险溢价的违约风险成分。在马尔可夫因子模型下，我们通过基于耦合半线性偏微分方程系统估计的不动点论证，建立了均值场BSDE的短时可解性。最后，我们表明，随着参与者数量趋于无穷大，由均值场BSDE刻画的风险溢价渐近地使市场出清。
英文摘要
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.
Comments46 pages
