On a multi-dimensional risk model with regime switching

We consider an insurer with n (n ≥ 2) classes of insurance business. The surplus process for each class of
insurance business is assumed to follow a compound Cox risk process. Assume that n surplus processes
are correlated with thinning dependence and regime switching. By summing up the n surplus processes
we obtain a correlated risk process. Upper bounds for the ruin probability under certain assumptions are
derived. The joint ruin probability for n classes of insurance business, the distribution of the number of the
ruined business classes in a finite time interval and the Laplace transform of the ruin time of the correlated
risk process are investigated. Some closed form results are obtained. Numerical examples are presented
to explain how the collection of insurance risk increases the solvency of an insurer.