A Constrained Profit Maximization Model for a Multi-Line Property/Liability Company

One of the decisions to be made by a multiline property/liability insurance company is the amount of business to be written in each of its product lines. This decision should reflect the profitability of each line, but should also be based on the relative capital requirements for each line mix alternative, as it is likely that the company has only a limited amount of capital to be used in support of insurance operations. The product mix choice then is one of constrained optimization, intended re achieve maximum expected profit given that the product mix must be allowable by the limited available capital. The traditional economic theory of the firm includes a model that determines the profit maximizing mix of outputs for a firm that has only one input to production (and a fixed amount thereof), but several possible outputs. This model can be adapted to the product mix question for a multiline property-liability company, by assuming that capital is the input, and that the earned premiums of the product lines are the outputs.