The qualitative behaviour of the optimal premium strategy is determined for an insurer in a finite and an infinite market using a deterministic general insurance model. The optimisation problem leads to a system of forward-backward differential equations obtained from Pontryagin's Maximum...

Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is...

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution...

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution...

The price of a general insurance policy for each insurer in a competitive non-cooperative market is determined by finding the Nash equilibrium of an N-player differential game. In this game, a demand law describes the relationship between policy sales and premium, and each insurer aims to...

Control theory is used to determine the optimal premium strategy for an insurer in order to maximise a given objective. Depending on the model parameters the optimal strategy can be loss-leading, which ultimately leads to negative premium values. This reflects the idea that it is optimal to...