Article Contents
Article Contents

# optimal investment and dividend policy in an insurance company: A varied bound for dividend rates

• In this paper we consider an optimal dividend problem for an insurance company whose surplus process evolves a classical ${\rm Cram\acute{e}r}$-Lundberg process. We impose a varied bound over the dividend rate to raise the dividend payment at a acceptable survival probability. Our objective is to find a strategy consisting of both investment and dividend payment which maximizes the cumulative expected discounted dividend payment until the ruin time. We show that the optimal value function is a unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with a given boundary condition. We characterize the optimal value function as the smallest viscosity supersolution of the HJB equation. We introduce a method to construct the potential solution of our problem and give a verification theorem to check its optimality. Finally we show some numerical results.

Mathematics Subject Classification: Primary: 35J87, 91B30, 49J20; Secondary: 49L25, 91B70, 49K20.

 Citation:

• Figure 1.  (a) The optimal value function. (b) The optimal dividend payment strategy. (c) The the optimal investment policy. (d) The first order derivative of $V(x)$

Figure 2.  Optimal value function for $p = 4$ and different $g$ restrictions

Figure 3.  Survival probability function under optimal strategy for $p = 2$ and different $g$ restrictions

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