Dynamic Portfolio Optimization Problems in Finance and Insurance.

这一建议推进了数学，重点是为银行和保险业制定更好的投资策略。主要目标是找到“简单”的策略，即用简单的数学术语来表达，以解决现实和困难的问题，从而更好地保护投资者免受当今复杂和快速变化的经济环境的影响。我的工作将创造第一个真正完整的分析投资策略沿着以下三个方向：·我将研究政府和机构法规（约束）对投资组合配置的影响，为银行和保险部门。我将建立在我最近的贡献约束投资组合问题的可解性，最初由欧洲的偿付能力II法规，市场风险模块的动机。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。我的目标是找到策略，最大限度地提高投资者的业绩，同时满足这些规定。·股票在金融市场中的行为近年来变得越来越复杂。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，例如：波动率的突然跳跃、相关性和波动率的波动性。我将开发先进的随机模型，能够捕捉这种行为与应用程序的投资组合优化。·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设定。我的目标是继续寻找对模型错误说明有弹性的投资策略（针对模棱两可的投资者）。能够最大限度地提高投资者业绩，同时考虑到上述三个方向的所有困难的投资战略将是一个真正全面的分析。我的研究结果将使研究人员能够从次优性能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：一旦采用最佳策略，他们可以节省多少钱。我希望这些结果能够产生重大影响，这要归功于对金融风险的更有效/准确的评估以及对法规影响的更深入理解。这将增加金融机构和监管机构之间的信任，从而为加拿大创造一个更健康的经济环境，并在全球范围内适用。 我计划在每年9名HQP的帮助下实施这一建议，这接近我目前每年7名的监督水平;我将继续确保和促进多元化和包容性的环境，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.