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Stochastic optimal control of DC pension funds. (English) Zbl 1141.91439
Summary: We study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy.
##### MSC:
 91B28 Finance etc. (MSC2000) 93E99 Stochastic systems and stochastic control
##### References:
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