Optimal strategies for pricing general insurance

Optimal premium pricing policies in a competitive insurance environment are investigated using approximation methods and simulation of sample paths. The market average premium is modelled as a diffusion process, with the premium as the control function and the maximisation of the expected total utility of wealth, over a finite time horizon, as the objective. In order to simplify the optimisation problem, a linear utility function is considered and two particular premium strategies are adopted. The first premium strategy is a linear function of the market average premium, while the second is a linear combination of the break-even premium and the market average premium. The optimal strategy is determined over the free parameters of each functional form. found that for both forms the optimal strategy is either to set a premium close to the break-even or not to sell insurance depending on the model parameters. If conditions are suitable for selling insurance then for the first premium strategy, in the case of no market average premium drift, the optimal premium rate is approximately p ̄ ( 0 ) / a T above break-even where p ̄ ( 0 ) is the initial market average premium, a is a constant related to the elasticity of demand and T is the time horizon. The optimal strategy for the second form of premium depends on the volatility of the market average premium. This leads to optimal strategies which generate substantial wealth since then the market average premium can be much larger than break-even leading to significant market exposure whilst simultaneously making a profit. Monte-Carlo simulation is used in order to study the parameter space in this case.