A model of pension portfolios with salary and surplus process
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Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a continuous time framework. The particular model is very much designed according to the members’ preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables.