Dividend maximisation in an insurance process compounded by risky and non-risky investments.

Abstract

Shareholders of an insurance company would expect maximum dividends from their investment in insurance companies for decades. Therefore, there is a need for managers of insurance companies to pay out appealing dividends to shareholders without compromising the company’s longevity in business. The commonest dividend payment strategy is the so-called barrier strategy. In this dissertation, I seek to determine the optimal barrier level for the payment of optimal dividends to shareholders. To achieve this, I consider an insurance company whose basic surplus follows the Cram´er-Lundberg model perturbed by diffusion and is allowed to invest in a financial market governed by the Black-Scholes model. A second-order IDE for the expected present value of all future dividends paid out before ruin is derived. For exponentially distributed claim sizes, the IDE is converted into an ODE with appropriate initial conditions. This is then converted into a system of first-order ODEs and solved using RK4. For claims that follow the Pareto distribution, the IDE is solved by replacing the derivatives with their finite difference approximations and the integral term approximated using the trapezoidal rule. The results obtained in this study are shown in Chapter 4. The optimal barrier levels have been computed for selected parameters that are commonly used in literature and the corresponding value function has also been determined. Graphs of the value function against initial capital have been drawn to confirm that the computed optimal barrier is indeed the correct one. The effect of investment on dividends paid to shareholders has also been investigated. Results indicate that dividends increase with investments in assets with a high rate of return. This is true for both heavy and light-tailed claim distributions.