This work addresses the issue of dividend payouts of an insurer whose
portfolio is exposed to insurance risk. The insurance risk arises from
the perturbed classical surplus process commonly known as the
Cramér-Lundberg model in the insurance literature. To enhance her
financial base, the insurer invests into assets whose price dynamics are
governed by a Black-Scholes model. We derive a linear Volterra
integral equation of the second kind and solve the equations for each
chosen barrier, thus generating corresponding dividend value
functions. We have obtained the optimal barrier that maximises the
expected discounted dividend payouts prior to ruin.