Pricing in the Multi Line Insurer with Dependent Gamma Distributed Risks allowing for Frictional Costs of Capital

This paper considers the pricing of insurance contracts for a multi- line insurer in a single period model where insurance risks have depen- dent gamma distributions. The pricing takes into account the impact of default, as well as financial distress costs arising from the possibilityof default by the insurer, and allocates these to line of business in an economically meaningful manner. The costs of capital include fric- tional costs arising from writing insurance business and are assumed to be proportional to insurer end of period capital. In practice these must be incorporated into by-line pricing by also allocating them to line of business. We develop closed form expressions for prices and the allocation of default and frictional costs of capital to lines of buisness based on assumptions used in the application of standard option pric- ing models to insurer balance sheets. These closed form expressions can be used to implement the model in practice.