Optimal Investment For Defined Contribution Plan Pension Under The Stochastic Volatility Model

With the rapid aging of world population, more and more attention is being paid tothe maintenance and appreciation of the value the old-age pension. While investment is acommonly adopted method to realize that, it entails risks. Therefore, an optimal investmentstrategy is necessary. In the actual financial market, there are many uncertain events, suchas foam, disaster, the financial crisis, all immensely impacting the earnings and varianceof risk assets. There are large numbers of empirical studies showing that the earnings andvariance of risk assets (for example, stocks) are random. Therefore, finding an optimalinvestment strategy for the pension plans, under a circumstance of random earnings andvariance of the risk assets, is of both theoretical and practical significance.In this paper, we study defined contribution pension plan under two circumstances: thepension fund as a risk-free asset and pension fund as a risky asset. An optimal investmentstrategies of DC pension plan maximizing the expected wealth is to be found. By applyingthe exponential utility function, power utility function and logarithmic utility function, weobtain the optimal investment strategy for maximizing the expected wealth and the explicitexpression of the Maximal Expected Wealth Utility Function as well.In this paper, we discussed diferent cases where the variance of risky assets are sub-ject to diferent models including the CEV stochastic volatility model, Heston stochasticvolatility model and the Stein-Stein stochastic volatility model. Chapters2,3and4re-spectively show how diferent optimal investment strategies are obtained under these threemodels. By solving for the HJB function corresponding to the objective function, the opti-mal investment strategy and the exact expression of the optimal function.