Dynamic Portfolio Optimization Problems in Finance and Insurance.

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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.