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Explicit solution of a general consumption/investment problem. (English) Zbl 0587.90012
Stochastic differential systems, Proc. 3rd Bad Honnef Conf. 1985, Lect. Notes Control Inf. Sci. 78, 209-216 (1986).
[For the entire collection see Zbl 0579.00014.] This talk shows how to solve a general consumption and investment decision problem in closed form. An investor seeks to maximize total expected discounted utility of consumption. There are N distinct risky investments, modelled by dependent geometric Brownian processes, and one riskless (deterministic) investment. The analysis allows for a general utility function and general rates of return. The model and analysis take into consideration the inherent nonnegativity of consumption and consider bankruptcy. The value function is determined explicitly, as are the optimal consumption and investment policies.
91B28Finance etc. (MSC2000)
91B62Growth models in economics
93E03General theory of stochastic systems