Abstract
We consider an investment/consumption model for economic agents each of whom has a HARA utility function and whose objective is maximization of the total expected utility of consumption. There is a diffusion process Y t which describes the random technology changes and whose state effects the fluctuations of the wealth of each of the agents. This model was considered by Cox, Ingersoll and Ross in the context of the problem of equilibrium asset prices. In this paper we establish the conditions of the existence of the classical solution to the corresponding Bellman equation and consider its dependence on the type of the utility functions the individual agent possesses.
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Huang, CF., Taksar, M., Zhu, S.H. (1999). A Verification Theorem in General Equilibrium Model of Asset Prices. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_35
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_35
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
Online ISBN: 978-1-4612-1784-8
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