  The present paper addresses the issue of choosing an optimal dynamic
reinsurance policy, which is state-dependent, for an insurance company that
operates under multiple insurance business lines. The optimal survival function
is characterized as the unique nondecreasing viscosity solution of the
associated Hamilton-Jacobi-Bellman equation (HJB) equation with limit one at
infinity. The finite difference method (FDM) has been utilized for the
numerical solution of the optimal survival function and optimal dynamic
reinsurance strategies and the proof for the convergence of the numerical
solution to the survival probability function is provided.
