英文标题：
《Time-inconsistency with rough volatility》
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作者：
Bingyan Han and Hoi Ying Wong
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最新提交年份：
2020
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英文摘要：
Motivated by recent advances in rough volatility, this paper investigates the impact of roughness on equilibrium feedback strategies for time-inconsistent objectives. Under a general framework embracing non-Markovian and non-semimartingale models, we develop an extended path-dependent Hamilton-Jacobi-Bellman (PHJB) equation system. A verification theorem is provided. By deriving explicit solutions to three problems, including mean-variance portfolio problem (MVP) with constant risk aversion, MVP for log-returns, and an investment/consumption problem with non-exponential discounting, we present that volatility roughness adjusts the equilibrium strategies considerably, up to 40% in certain settings. Since rough volatility models capture the near-term downside risk by fitting the volatility skews, we interpret the adjustments as a hedge for this risk.
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中文摘要：
基于粗糙波动率的最新进展，本文研究了粗糙度对时间不一致目标均衡反馈策略的影响。在包含非马尔可夫和非半鞅模型的一般框架下，我们发展了一个扩展的路径相关Hamilton-Jacobi-Bellman（PHJB）方程组。给出了一个验证定理。通过推导三个问题的显式解，包括具有常数风险厌恶的均值-方差投资组合问题（MVP）、对数收益的MVP和具有非指数贴现的投资/消费问题，我们提出波动粗糙度可以显著调整均衡策略，在某些情况下高达40%。由于粗糙波动率模型通过拟合波动率偏斜来捕捉短期下行风险，我们将调整解释为对该风险的对冲。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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