One attractive objective for a pensioner using the income drawdown option is to minimise the deviation of the pension fund from a prescribed deterministic target. Typically, this problem is formulated as a linear-quadratic optimal control problem, which has the shortcoming that over-performance...

A two factor stochastic model is introduced for the two phases of a defined-contribution pension scheme. During the accumulation phase of the pension, the scheme member invests part of their stochastic income in a portfolio of a risky stock and a bond in order to build up sufficient funds for...

A simple parametrization is introduced which represents the insurance market's response to an insurer adopting a pricing strategy determined via optimal control theory. Claims are modeled using a lognormally distributed mean claim size rate and the market average premium is determined via the...

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...

During the accumulation phase of a defined-contribution pension scheme, a scheme member invests part of their stochastic income in a portfolio of a stock and a bond in order to build up sufficient funds for retirement. It is assumed that the remainder of their salary pre-retirement is consumed,...

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...