Intergenerational risk sharing of pension schemes under modified utility function

In this paper, I want to do some research in the paper: Intergenerational risk sharing within funded pension schemes (Jiajia Cui, Frank de Jong and Eduard Ponds, 2011) published on Journal of Pension Economics and Finance. The original paper mainly studies the risk sharing between generations in different kinds of funded pension schemes. At first, I build models and simulate them via Matlab software to replicate the path used in this paper, in order to find out the methods and verify the results. After that, I make some changes of the utility function used in the paper for searching the optimization point for some funded pension schemes. Instead of the traditional CRRA (constant relative risk aversion) model, I want to change the CRRA utility function from constant risk aversion rate ( ) to a function containing different risk aversion parameters ( ) for different age cohort. Expectedly, the new optimal points we get might have difference compared with ones in the original paper, and we might get some new observations of performance of different pension schemes. Besides, for participations of different kinds of funded pension schemes, their risk aversion parameter ( ) might change due to the different income styles, and this should be taken into consideration when comparing risk sharing between generations. Moreover, if using this change into models which calculate the investment allocation, the percentage of investment in risky and riskless asset should be change conceptually.