Before revision:  The case of unrestricted payment scheme gives rise to a singular stochastic control problem. By solving the associated integro-differential quasi-variational inequality,  the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions.
After revision:  The case of unrestricted payment scheme , by solving the associated integro-differential quasi-variational inequality, the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions.