Dynamic Portfolio Optimization Problems in Finance and Insurance.

这一建议推进数学，重点是为银行和保险部门制定更好的投资策略。关键目标是找到“简单”的策略，即用简单的数学术语表达，以解决现实和困难的问题，使投资者在当今复杂和迅速变化的经济环境中得到更好的保护。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法规（约束）对投资组合配置的影响，对于银行和保险部门。我将以我最近对受限投资组合问题的可解决性的贡献为基础，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，使投资者的业绩最大化的策略。·近年来，金融市场上股票的行为变得越来越复杂。这可以通过文献中越来越多的所谓“程式化事实”来观察，例如：波动性的突然跳跃、相关性和波动性的波动性。我将开发先进的随机模型，能够捕捉这些行为，并将其应用于投资组合优化。·我将考虑到许多定义标准模型和新模型的参数很难从数据中校准这一事实。这种模型参数的不确定性被称为模型错配。我的目标是继续寻找能够适应模型错误规范的投资策略（针对不喜欢模糊性的投资者）。在考虑到上述三个方向的所有困难的同时，能够使投资者业绩最大化的投资策略才是真正全面的分析。我的研究结果将允许研究人员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，由于对金融风险的更有效/准确的评估以及对监管影响的更深入理解，这些结果将产生重大影响。这将增加金融机构之间以及与监管机构之间的信任，从而使加拿大的经济环境更加健康，适用于全球。我计划在每年9个HQP的帮助下实施这个提案，这接近我目前每年7个的监管水平；我将继续确保和促进一个多元化和包容的环境，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.