  In this paper, we examine the effect of background risk on portfolio
selection and optimal reinsurance design under the criterion of maximizing the
probability of reaching a goal. Following the literature, we adopt dependence
uncertainty to model the dependence ambiguity between financial risk (or
insurable risk) and background risk. Because the goal-reaching objective
function is non-concave, these two problems bring highly unconventional and
challenging issues for which classical optimization techniques often fail.
Using quantile formulation method, we derive the optimal solutions explicitly.
The results show that the presence of background risk does not alter the shape
of the solution but instead changes the parameter value of the solution.
Finally, numerical examples are given to illustrate the results and verify the
robustness of our solutions.
