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。关键目标是找到解决现实和困难问题的“简单”策略，即用简单的数学术语表示，以便投资者在当今复杂和迅速变化的经济格局中得到更好的保护。我的工作将沿着以下三个方向创建第一个真正完整的投资策略分析：·我将研究政府和机构监管(约束)对投资组合配置的影响，对银行和保险行业。我将以我最近对受限投资组合问题的可解性的贡献为基础，这些问题最初是由欧洲的偿付能力II法规--市场风险模块--推动的。我计划研究LICAT法规(加拿大保险业，从市场风险模块开始)和银行业巴塞尔III规则混合产生的约束问题。我的目标是找到在满足这些规定的同时，为投资者实现业绩最大化的策略。·最近一段时间，金融市场的股票行为变得更加复杂。这可以通过文献中报道的越来越多的所谓“程式化事实”来观察到，例如：波动率、相关性和波动率的突然跳跃。我将开发能够捕捉这种行为的高级随机模型，并将其应用于投资组合优化。·我将考虑到这样一个事实，即定义标准和新模型的许多参数很难从数据中校准。模型参数的这种不确定性被称为模型误指定。我的目标是继续寻找对模型错误说明有弹性的投资策略(目标是避免模棱两可的投资者)。能够在考虑到前三个方向所述所有困难的同时使投资者业绩最大化的投资策略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研究许多流行的策略，即投资者将能够回答这个问题：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。我计划每年在9个HQP的帮助下实施这项建议，这接近我目前每年7个的监督水平；我将继续确保和促进一个多样化和包容性的环境，这是培养创造力和创新的基础。

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 economic landscape. My work will create the first truly integral analysis of investment strategies along the following three directions: · I will study the implications of government and institutional regulations (constraints) on portfolio allocation, for the banking and insurance sectors. I will build on my recent contributions to the solvability of constrained portfolio problems, originally motivated by European's Solvency II regulations, the market risk module. I plan to study the constrained problems derived from a mixture of LICAT regulations (Canadian Insurance sector, starting with the market risk module), and Basel III rules from the banking sector. My objective is to find strategies that maximize the performance for investors while fulfilling these regulations. · The behavior of stocks in financial markets is becoming more complex in 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, correlations, and volatility of volatility. I will develop advanced stochastic models capable of capturing such behaviors with applications to portfolio optimization. · I will take into account the fact that many of the parameters defining standard and new models are difficult to calibrate from data. This uncertainty on the parameters of the model is known as model misspecification. My objective is to continue finding investment strategies that are resilient to model mis-specification (aiming at ambiguity-averse investors). 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 popular 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. I plan to implement this proposal with the help of 9 HQP per year, this is close to my current supervisory level of 7 per year; I will continue ensuring and promoting a diverse and inclusive environment, fundamental to fostering creativity and innovation.