Estimates for the optimal control policy in the presence of regulations and heavy tails

We consider a classical heavy tailed risk model, included in a regulation mechanism. The regulator exercises a minimal cash requirement level and penalties for violating it to regulate the insurance firm. The problem of the insurance firm is to establish an investment and risk exposure policy as well as a barrier dividend strategy, which is a function of the strategy used by the regulator. For regularly varying tailed claim size distributions, we find the asymptotics of the stationary distribution of the risk model and derive fundamental asymptotic results of the insurance firm's problem. In the special case of Pareto claim size distributions, the asymptotic optimal control policy is found in closed form, as well as numerical results.