Determination of Optimum Fair Premiums in Property-Liability Insurance: An Optimal Control Theoretic Approach

Dynamic valuation models for the computation of optimum fair premiums are developed using a new framework. The concept of fair premiums which are also “best” is introduced. Optimum fair premiums are defined as the minimum discounted losses for an insurance firm or industry. This notion extends the discrete and continuous discounted cash flow models in many ways. The problem is cast in an optimal control theoretic setting that assumes a world of certainty. It is then extended to incorporate uncertainty in claims occurrence. Using a simple example of the certainty model, a closed-form formula for the rate of return for an insurer or investor is derived. We show that the optimum competitive equilibrium price is the sum of the marginal cost of claims and an economic rent to the insurer.