A data driven approach for optimal stochastic control in finance

金融中的许多问题都是随机最优控制问题，包括最优交易执行、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随机最优控制问题所产生的金融。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建最优控制。为了理解这种新范式的问题，我们将用这种方法来解决金融中的三个问题。第一个测试问题将涉及在一个较长的时间框架内与应税账户的投资组合的最佳多期再平衡。在这些多个再平衡时间的每一个都需要考虑税收情景，如边际税率，资本收益和资本损失。第二项研究将涉及最佳多期投资组合再平衡的时间，我们寻求最佳的再平衡时间和在这些时间内重新分配的金额。我们最后的研究涉及的投资组合策略，结合了单一资产的出售期权，平衡了涉及一篮子资产的趋势跟踪概念。这里需要找到每个部分的最佳权重。加拿大是机器学习和人工智能的世界领导者。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。这是尤其如此，当涉及到管理与长期投资分配问题所涉及的风险。

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 truewhen it comes to managing the risks involved with long term investment allocation problems.