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 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.