Insurance Exposure and Investment Risks: An Analysis Using Chance-Constrained Programming

By exposing itself to greater risks on the invested funds, the company can also increase its expected returns. Because there are risks involved with both the insurance and investment operations, a major problem for a company is to determine just how the two types of risks are to be balanced. This paper formulates the premium-volume/investment-mix problem for nonlife-insurance companies as a chance-constrained programming problem. A number of numerical examples of the model were run to assess the effects of investment risks, insurance risks, and the willingness of the company to tolerate risks. The paper derives the conclusion that risks in both investment possibilities and insurance portfolios are compensated for, to a large extent, by varying the growth rate of premiums, in addition to shifts in portfolio makeup. The two problems—growth and portfolio selection—cannot and should not be separated. The paper shows that the traditional rules of thumb—e.g., if the premium-surplus ratio is high, the common-stock portion of the investment portfolio should be low—are somewhat ambiguous and not borne out by the numerical examples.