Various stakeholders in finance and insurance—such as regulators, investors and managers—rely on quantitative analysis in their decision-making processes. This research project employs quantitative models and methods from probability theory and statistics to tackle problems that are of practical relevance in these fields. Three topics are mainly concerned.  The first topic studies numerical techniques that are useful in financial and actuarial valuation such as option pricing, capital allocation and risk aggregation etc. We aim to propose new efficient computational methods and techniques. The second topic studies investment strategies and behaviors under general risk preference with emphasis on portfolio selection, skewness preference and performance measure etc. The third topic delves into dependence modeling of risks and its applications in finance and insurance. It covers popular research questions such as model uncertainty, systemic risk, high-dimensional risk measure and worst-scenario analysis etc.