This study examines optimal investment and reinsurance policies for an insurer with the classical
surplus process. It assumes that the financial market is driven by a drifted Brownian motion with
coefficients modulated by an external Markov process specified by the solution to a stochastic
differential equation. The goal of the insurer is to maximize the expected terminal utility. This
paper derives the Hamilton-Jacobi-Bellman (HJB) equation associated with the control problem
using a dynamic programming method. When the insurer admits an exponential utility function,
we prove that there exists a unique and smooth solution to the HJB equation. We derive the
explicit optimal investment policy by solving the HJB equation. We can also find that the
optimal reinsurance policy optimizes a deterministic function. We also obtain the upper bound
for ruin probability in finite time for the insurer when the insurer adopts optimal policies.

Optimal investment; Reinsurance; Markov modulated risk model; HJB equa

Anhui Normal University; Nanjing University of Finance & Economics