  In this paper, we study an optimal reinsurance-investment problem in a risk
model with two dependent classes of insurance business, where the two claim
number processes are correlated through a common shock component. We assume
that the insurer can purchase per-loss reinsurance for each line of business
and invest its surplus in a financial market consisting of a risk-free asset
and a risky asset. Under the criterion of minimizing the probability of
drawdown, the closed-form expressions of the optimal reinsurance-investment
strategy and the corresponding value function are obtained. We show that the
optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance
strategy under the expected value principle, and under the variance premium
principle, the optimal reinsurance strategy is in the form of pure quota-share
reinsurance. Furthermore, we extend our model to the case where the insurance
company involves $n$ $(n\geq3)$ dependent classes of insurance business and the
optimal results are derived explicitly as well.
