Abstract
This study addresses the issue of maximization of dividends of an insurer whose portfolio is exposed to insurance risk. The insurance risk arises from the classical surplus process commonly known as the Cramer-Lundberg model in the insurance literature. To enhance his financial base, the insurer invests in a risk free asset whose price dynamics are governed by a constant force of interest. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method of Paulsen et al.[1] in conjunction with the Simpson rule to solve the Volterra integral equations for each chosen barrier thus generating corresponding dividend value functions. We have obtained the optimal barrier that maximizes the dividends. In the absence of the financial world, the analytical solution has been used to assess the accuracy of our results.
Highlights
We concentrate on barrier strategies in this study they may not be optimal when compoundedThe model we consider in this study derives its by a diffusion in a vibrant financial market in which name from the path breaking work of Lundberg [2] and case other strategies e.g. b and strategies take an upperCramér [3,4,5]
We study the expected discounted dividend payments prior to ruin with δ as the discount factor when the model (1) is compounded
De Finetti[7] underscored the importance of dividend payments in the economic considerations and management of insurance companies
Summary
We concentrate on barrier strategies in this study they may not be optimal when compoundedThe model we consider in this study derives its by a diffusion in a vibrant financial market in which name from the path breaking work of Lundberg [2] and case other strategies e.g. b and strategies take an upperCramér [3,4,5]. We study the expected discounted dividend payments prior to ruin with δ as the discount factor when the model (1) is compounded Dividend barrier models have a long history of risk theory [8,9,10]. We numerically compute the same dividend value functions using the block-by-block method developed in Paulsen et al.[1] and compare the results.
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