Optimal Dividend and Issuance of Equity Policies in the Presence of Interest

Abstract

We investigate the dividend and equity issuance problem in the presence of interest rate. The evolution of the financial reserves of an insurance company, where management payout dividends and issue new equity, is described by a stochastic differential equation. The work of Lokka and Zervos [1] is extended by including the interest rate component into the model in order to make the model more realistic. The aim is to maximise the expected discounted dividends pay-out until the time of bankruptcy. In order to investigate this problem, the stochastic control theory for diffusion processes will be used. In order to handle the problem, the Hamilton-Jacobi-Bellman equation (HJB) is derived and solved. The second order ordinary differential equation associated with the problem turns out to belong to the class of Kummer's confluent hyper-geometric differential equations. This category of equations is not easy to solve. The equation is non-dimensionalised and change of variables is effected in two different stages. The results show that interest rate affected the rate at which the value function and threshold level change.