  In this paper, we investigate the problem of optimal strategies of dividend
and reinsurance under the Cram\'{e}r-Lundberg risk model embedded with the
thinning-dependence structure which was firstly introduced by Wang and Yuen
(2005), subject to the optimality criteria of maximizing the expected
accumulated discounted dividends paid until ruin. To enhance the practical
relevance of the optimal dividend and reinsurance problem, non-cheap
reinsurance is considered and transaction costs and taxes are imposed on
dividends, which converts our optimization problem into a mixed
classical-impulse control problem. For the purpose of better mathematical
tractability and neat, explicit solutions of our control problem, instead of
the Cram\'er-Lundberg framework we study its approximated diffusion model with
two thinly dependent classes of insurance businesses. Using a method of
quasi-variational inequalities, we show that the optimal reinsurance follows a
two-dimensional excess-of-loss reinsurance strategy, and, the optimal dividend
strategy turns out to be an impulse dividend strategy with an upper and a lower
barrier, i.e., every thing above the lower barrier is paid as dividends each
time the surplus is above the upper barrier, otherwise no dividends are paid.
Closed-form expression for the value function associated with the optimal
dividend and reinsurance strategy is also given. In addition, some numerical
examples are presented to illustrate the optimality results.
