具有状态切换和违约传染的最优信贷组合与消费
Optimal credit portfolio and consumption with regime switching and default contagion
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中文总结 AI 辅助
研究具有违约传染的状态切换多名称信贷市场的最优投资组合和消费问题，利用柯布-道格拉斯效用将HJB方程简化，通过向后求解建立正古典解相关性质，刻画最优反馈控制并证明验证定理。
中文摘要 AI 辅助
我们研究了具有违约传染的状态切换多名称信贷市场中的最优投资组合和消费。违约会造成投资组合损失并改变存续证券的强度。在柯布-道格拉斯效用下，齐次性将HJB方程简化为一个由违约状态索引的递归常微分方程组。从全违约状态向后求解，我们建立了正古典解的存在性和唯一性，刻画了最优反馈控制，并证明了一个验证定理。
英文摘要
We study an optimal portfolio and consumption problem in a regime-switching multi-name credit market with default contagion. Default events not only generate direct portfolio losses but also alter the default intensities of surviving securities. Under a Cobb-Douglas utility, the homogeneity property reduces the associated Hamilton-Jacobi-Bellman (HJB) equation to a recursive system of ordinary differential equations indexed by the default states. Solving this system backward from the all-default state, we establish existence and uniqueness of a positive classical solution, characterize the optimal feedback controls, and provide a verification theorem. Finally, numerical experiments present sensitivity analyses and comparisons across contagion settings, regimes, utilities, as well as before and after default.
发表机构
- Wuyi University（五邑大学）
- Fujian Normal University（福建师范大学）
- Xi’an Jiaotong University（西安交通大学）
- Xiamen University（厦门大学）
机构由 AI 辅助整理，请以论文原文为准。
