发表机构
CMAP, École Polytechnique; Department of Statistics, University of Warwick; Institut für Stochastik und Anwendungen, University of Stuttgart（巴黎综合理工学院; 华威大学统计学系; 斯图加特大学随机数学与应用研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对连续金融市场，提出基于积分方差时钟的随机框架，通过IVC-BSDEs刻画最优投资与消费策略，并推广至粗糙Volterra Heston模型，统一了现有结果。
AI 中文摘要
我们研究了一类一般连续金融市场中的无限期最优投资与消费问题，其中不确定性由表示累积方差的连续非降随机时钟驱动。该框架涵盖了经典马尔可夫和非马尔可夫随机波动率模型，以及不存在瞬时波动率过程的奇异已实现方差模型。我们通过一个由日历时间和随机时钟共同驱动的非线性无限期倒向随机微分方程来刻画价值过程以及最优投资和消费策略。我们基于上、下解方法为该新类IVC-BSDEs建立了一般适定性理论，在自然条件下确立了存在性、唯一性和稳定性，这些条件在金融应用之外可能具有独立意义。此外，我们利用Malliavin演算确定了解的Z分量的符号。然后，我们将结果应用于具有局部可积核的Volterra Heston模型，涵盖粗糙和超粗糙情形。利用模型的仿射结构，我们在不完全市场中验证了候选策略的最优性，并在完全市场情形下获得了解的显式表示。由于框架的普遍性以及对随机时钟施加的弱假设，我们的结果统一并推广了若干现有的最优投资与消费结果，包括经典马尔可夫随机波动率模型。
英文摘要
We study the infinite-horizon optimal investment and consumption problem in a general class of continuous financial markets, where uncertainty is driven by a continuous non-decreasing stochastic clock representing accumulated variance. This framework encompasses classical Markovian and non-Markovian stochastic volatility models as well as singular realized-variance models in which no spot volatility process exists. We characterize the value process and optimal investment and consumption strategies in terms of a non-linear infinite-horizon backward stochastic differential equation driven jointly by calendar time and the stochastic clock. We develop a general well-posedness theory for this new class of IVC-BSDEs based on the method of sub- and supersolutions, establishing existence, uniqueness, and stability under natural conditions that might be of independent interest beyond the financial application at hand. We are moreover able to identify the sign of the $Z$-component of the solution using Malliavin calculus. We then apply our results to Volterra Heston models with locally integrable kernels, covering both rough and hyper-rough regimes. Exploiting the affine structure of the model, we verify the optimality of the candidate strategies in incomplete markets and obtain an explicit representation of the solution in the complete market case. Owing to the generality of the framework and the weak assumptions imposed on the stochastic clock, our results unify and extend several existing results for optimal investment and consumption, including classical Markovian stochastic volatility models.
