Notions of Dependence with Applications in Insurance and Finance
Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.