  This paper investigates the optimal management of an aggregated defined
benefit pension plan in a stochastic environment. The interest rate follows the
Ornstein-Uhlenbeck model, the benefits follow the geometric Brownian motion
while the contribution rate is determined by the spread method of fund
amortization. The pension manager invests in the financial market with three
assets: cash, bond and stock. Regardless of the initial status of the plan, we
suppose that the pension fund may become underfunded or overfunded in the
planning horizon. The optimization goal of the manager is to maximize the
expected utility in the overfunded region minus the weighted solvency risk in
the underfunded region. By introducing an auxiliary process and related
equivalent optimization problems and using the martingale method, the optimal
wealth process, optimal portfolio and efficient frontier are obtained under
four cases (high tolerance towards solvency risk, low tolerance towards
solvency risk, a specific lower bound, and high lower bound). Moreover, we also
obtain the probabilities that the optimal terminal wealth falls in the
overfunded and underfunded regions. At last, we present numerical analyses to
illustrate the manager's economic behaviors.
