A data driven approach for optimal stochastic control in finance

金融中的许多问题自然会以随机最优控制问题的形式出现，例如最优交易执行、可变年金的定价和对冲以及多期资产配置。我们将研究一种新的、数据驱动的方法来处理这种来自金融的随机最优控制问题。特别是，我们建议使用机器学习方法直接从观察到的数据构造最优控制。为了理解这种新范式的问题，我们将在金融中的三个问题上使用这种方法。第一个测试问题将涉及在长期框架内对应纳税账户的投资组合进行最佳的多期再平衡。在每一次多重再平衡时，都需要考虑边际税率、资本利得和资本损失等税收情景。**第二项研究将涉及最佳多期投资组合再平衡的时机，我们寻求再平衡的最佳时间和在这些时间内重新配置的金额。我们最后的研究涉及投资组合的策略，该策略结合了单一资产的出售期权，通过涉及一篮子资产的趋势跟随概念来平衡。这里需要找到每个部分的最佳权重。加拿大在机器学习和人工智能方面处于世界领先地位。金融科技（FinTech）领域将受益于更好的数据分析和更有效的学习方法。当涉及到管理长期投资分配问题所涉及的风险时，这一点尤其正确。

Many problems in finance naturally arise as stochastic optimal control problems, including for example optimal trade execution, pricing and hedging of variable annuities and multi-period asset allocation. We will investigate a new, data driven approach to handling such stochastic optimal control problems arising from finance. In particular, we propose to use a machine learning approach to constructing the optimal controls directly from the observed data. To understand the issues of this new paradigm, we will use this approach on three problems in finance. The first test problem will involve the optimal multi-period rebalancing of portfolios over a long time frame with taxable accounts. At each of these multiple rebalancing times one would need to take into consideration tax scenarios such as marginal tax rates, capital gains and capital losses.**The second study will involve the timing of optimal multi-period portfolio rebalancing where we seek both optimal times to rebalance and the amounts to reallocate during these times. Our final study involves strategies for portfolios that combines selling options on single assets balanced by the concept of trend following involving baskets of assets. Here one needs to find the best weighting of each part. Canada is a world leader in Machine Learning and AI. The field of financial technology (FinTech) is one area which will benefit from better data analytics and more effective learning methods. This is particularly true**when it comes to managing the risks involved with long term investment allocation problems.