发表机构
McCloud Research（麦克劳德研究）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出熵风险优化框架用于不完备市场衍生品定价与对冲，在二次高斯模型下获得闭式解，将损益分解为市场与模型风险，并支持深度对冲回归。
AI 中文摘要
熵风险优化是一个在不完备市场中定价和对冲金融衍生品的通用框架，可用于将损益分解为市场和模型风险贡献。当价格服从二次高斯模型时，价格和对冲比率的耦合方程可得到闭式解。这使得能够全面分析交易损益，并将模型风险价值分解为凸性、维度和融资贡献，这些贡献被归因于对已实现损益的解释。当标的价格遵循高斯过程（如分数奥恩斯坦-乌伦贝克过程）时，二次高斯模型的方程可直接适用。该模型还为对冲比率提供了简单的参数表达式，可用于深度对冲中的回归分析。
英文摘要
Entropic risk optimisation is a general framework for pricing and hedging financial derivatives in incomplete markets that can be used to decompose P&L into market and model risk contributions. When the prices are quadratic Gaussian, the coupled equations for price and hedge ratios are solved in closed form. This enables comprehensive analysis of trading P&L, with a decomposition of the model value-at-risk into convexity, dimension and funding contributions that are attributed in the explanation of realised P&L. The equations of the quadratic Gaussian model are directly applicable when the underlying prices follow Gaussian processes, such as fractional Ornstein-Uhlenbeck processes. The model also provides simple parametric expressions for hedge ratios that can be used for regressions in deep hedging.
CommentsPresented at QuantMinds 2026
