Optimal Contribution and Investment in a Defined Benefit Pension Plan When the Return Rate of Risky Assets is Time Series Correlated and Cyclical Change

This work considers stochastic models of defined benefit pension plans. Stochastic growth rate of salary, and stochastic mortality is allowed to evaluate pension plan. Especially important thing is that based on Momon (2004), we extend Vasicek model to multi-dimentional cases and use it to mode the return rates of multi-risky assets invested and the growth rate of wage with time series correlation and cyclically changes. we apply time inconsistent dynamic programming and establish objective function of minimizing the sum of the valatilities of the contribution and the return rate of investment portfolio in order to determine dynamically optimal contribution rate and investment strategy.