Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary

We follow up our earlier work [Insurance: Math. Econ. 15, (1994) 151-162], which introduced the methods of finite control optimisation to the problem of pension funding for a defined benefit pension scheme, where valuations are carried out on a short-term, winding-up valuation basis. The model involves a linear stochastic dynamic system with a quadratic optimisation criterion (i.e. an LQP problem), and the solution is based on optimal control theory. The current paper extends this work by deriving, in relation to a long-term, going-concern valuation basis, optimal funding control procedures over an infinite control horizon, making use of the monotone convergence property of the dynamic programming algorithm. The stochastic inputs modelled are the investment rates of return and benefit outgoes, both of which are assumed to be stationary. As a result, we believe that the optimal funding policy derived could provide a stationary long-term guideline for the funding of public employees' pension systems.