Explicit solution of a general consumption/investment problem
Mathematics of Operations Research
Optimal portfolio and consumption decisions for a “small investor” on a finite horizon
SIAM Journal on Control and Optimization
Optimization by Vector Space Methods
Optimization by Vector Space Methods
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We study a maximization problem from terminal wealth and consumption for a class of robust utility functions introduced in Bordigoni, Matoussi, and Schweizer [A stochastic control approach to a robust utility maximization problem, in Stochastic Analysis and Applications, Abel Symp. 2, F. E. Benth, G. Di Nunno, T. Lindstrøm, B. Øksendal, and T. Zhang, eds., Springer, Berlin, 2007, pp. 125-151]. Our method is based on backward stochastic differential equation theory techniques. We prove a dynamic maximum principle for the optimal control. We study the existence and the uniqueness of the consumption-investment strategy which is characterized as the unique solution of a forward-backward system.