2006/03/14 by Jaime A. Londoño, Londoño, Jaime A.
Economics, Econometrics and Finance · #91B16 #91B28 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.math/0603316
openalex publication_date 2006/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is one proposed by the author in Dynamic State Tameness arXiv:math.PR/0509139. The proposed framework is a generalization of the theory of Brownian flows and can be applied to those processes that are the solutions of classical Ito stochastic differential equations, even when the volatilities and drifts are just locally δ-Holder continuous for some δ>0. We develop the martingale methodology for the solution of the problem of optimal consumption and investment. Complete solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities in the current literature, and consider general restrictions on minimal wealths. As a secondary result we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies.