Pension plans in the United States come in two varieties. Defined contribution pension plans specify the contribution of the Corporation. The employees have the right to invest the corporation’s contribution and their own contribution in a limited set of funds. The participants in a defined contribution pension plan are responsible for making all the investment decisions and bear all the risks associated with these decisions; thus, the benefit to the participants is uncertain. In contrast, defined benefit pension plans specify the benefits due to plan participants. The plan Sponsor, that is the corporation, makes all the Investment decisions in a defined benefit pension plan and bears all the investment risk. Defined benefit plans have been in the news in the past few years because some firms face the prospect of bankruptcy over severely underfunded pension plans. Consequently there is a need to develop models that account for uncertainty in future market conditions and plan accordingly.