| dc.description.abstract | In the optimal risk model, people usually are concerned about the dependent risks to explore how the optimal reinsurance contracts vary with the degree of dependence. In this thesis, we investigate this problem in bivariate case using value-at-risk as risk measure further. There is no bundling of the two risks, and each risk is insured under a separate reinsurance contract. It is possible to formulate the optimization problem as an optimization task with two variables, subject to a single constraint. Specifically, we present an efficient method for estimating optimal contracts using importance sampling. The dependence is modeled using a Gaussian copula. The optimal solution is evaluated by the constraint curves and iso-curves of the objective function. The methods will be illustrated on a suitable set of examples, including symmetric and asymmetric cases as well as mixtures of distributions from Pareto, lognormal, truncated normal and gamma distributions. The optimal reinsurance contract relies on the correlation coefficient and the hazard rates of the risk distributions. With the increase in correlation coefficient, the optimal solution for symmetric risks will eventually be the balanced solution which means the insurance layer contracts should be chosen. However, the optimal solution is usually unbalanced for asymmetric risks for changing correlation coefficients. Furthermore, the more asymmetric the risks are, the closer the optimal solution is to the boundary and, therefore, the better the lighter-tailed risk should be covered by a stop-loss contract. | eng |