Abstract
This paper applies the maximum principle to obtain Hamilton-Jocabi-Bellman (HJB) equation for the asset and liability management problem under stochastic interest rate. And the optimal investment strategies under the Ho-Lee model and the Vasicek model are investigated respectively. Logarithm utility function is taken as the risky preference of investors and the closed-form solutions of the optimal investment strategy are derived via adopting Legendre transform approach.
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