Dynamic Portfolio Optimization Problems in Finance and Insurance.

这项提议推进了数学计算，重点是为银行和保险行业制定更好的投资策略。主要目标是找到“简单”的策略，即可以用简单的数学术语来表达，以解决现实和困难的问题，以便投资者在当今复杂和迅速变化的情况下得到更好的保护。我的工作将沿着以下三个方向对新的投资战略进行真正完整的分析：*·应对保险和银行业日益增长的政府和机构监管，例如：针对加拿大保险公司的LICAT(2018年生效)、针对欧洲保险公司的偿付能力II(2016年生效)以及针对全球银行业的巴塞尔III(2013)。我的目标是找到在满足监管规定的同时，为投资者带来最大收益的策略。*·最近金融市场的股票行为正变得更加复杂。这可以从文献中报道的越来越多的所谓“程式化事实”中观察到，例如：波动性和相关性的突然跳跃。我将开发能够捕捉这些新行为的高级随机模型，并将找到从中受益的投资策略。*·我将考虑这样一个事实，即定义标准模型和新模型的许多参数真的很难从数据中估计出来。模型参数上的这种不确定性称为模棱两可或模型错误说明。我的目标是继续寻找对模型错误指定有弹性的投资策略。*能够最大化投资者业绩的投资策略，同时考虑到前面三个方向所描述的所有困难，将是真正全面的分析。我的结果将使研究人员能够从次优表现的角度来研究许多当前使用的策略，即投资者将能够回答这样一个问题：一旦采用最优策略，他们可以节省多少钱。我预计这些结果将产生重大影响，这要归功于对金融风险的更有效/更准确的评估，以及对监管影响的更深入理解。这将增加金融机构和监管机构之间的信任，导致加拿大更健康的经济环境，适用于全球。

This proposal advances mathematics with a focus on developing better investment strategies for the banking and insurance sectors. The key objective is to find "simple" strategies, i.e. expressible in simple mathematical terms, to realistic and difficult problems such that investors are better protected against today's complex and rapidly changing circumstances. My work will provide a truly integral analysis of new investment strategies along the following three directions:******· Tackle increasing presence of government and institutional regulations in the insurance and banking sectors, like for example: LICAT for Canadian Insurance companies (effective 2018), Solvency II (effective 2016) for European insurance companies and Basel III (2013) for the banking sector worldwide. My objective is to find strategies that maximize the performance for investors while fulfilling regulations.***· The behaviour of stocks in financial markets is becoming more complex in the recent times. This can be observed via the increasing number of so called "stylized facts" reported in the literature, for example: sudden jumps in volatilities and correlations. I will develop advanced stochastic models capable of capturing these new behaviours and will find investment strategies that benefit from it.***· I will take into account the fact that many of the parameters defining standard and new models are really difficult to estimate from data. This uncertainty on the parameters of the model is known as ambiguity or model misspecification. My objective is to continue finding investment strategies that are resilient to model mis-specification.******Investment strategies capable of maximizing investor performance while taking all the difficulties described on the previous three directions into account would be a truly comprehensive analysis. My results would allow researchers to study many currently used strategies from the viewpoint of a suboptimal performance, i.e. Investors will be able to answer the question: how much they can save once optimal strategies are adopted. I expect these results to have a significant impact thanks to more efficient/accurate assessment of financial risks and a deeper understanding of the impact of regulations. This will increase trust among financial institutions and with regulators, leading to a healthier economic environment in Canada, applicable globally.