Kernel Learning for Mean-Variance Trading Strategies

Trading strategy construction and portfolio choice is a fundamental problem in quantitative finance, where traders and researchers aim to balance maximising PnL with the associated constraints that they face such as the information they are in possession of, volatility, liquidity and the associated costs of trading. In this work, we are concerned with finding optimal dynamic, path-dependent trading strategies in which the past trajectory of information is incorporated into the decision making as new information filters in. In particular, we solve an optimal portfolio choice problem where the inventory (position) is given as the control variate and derive a solution to the mean-variance criterion. Path-dependencies are ubiquitous in finance. They are present both in the underlying asset time series, either arising due to path-dependent volatility [Guy14; GL22] or due to price discovery (stochastic drift) as market participants react to diverse sources of information that arrives at differing speeds [Tót+11; Con+14; Oha15].