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A stochastic control approach to portfolio problems with stochastic interest rates. (English) Zbl 1020.93029

This paper regards investment problems with investing in a savings account, stocks, and bonds, and maximizing the utility from terminal wealth. Stochastic interest rates are assumed in contrast to the classical Merton model. The corresponding control problem is solved by proving a verification theorem without the usual Lipschitz assumptions.

MSC:

93E20 Optimal stochastic control
91G80 Financial applications of other theories
60H30 Applications of stochastic analysis (to PDEs, etc.)
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