Inconsistent Investment and Consumption Problems
In a traditional Black–Scholes market we develop a verification theorem for a general class of investment and consumption problems where the standard dynamic programming principle does not hold. The theorem is an extension of the standard Hamilton–Jacobi–Bellman equation in the form of a system of nonlinear differential equations. We derive the optimal investment and consumption strategy for a meanvariance investor without precommitment endowed with labor income. In the case of constant risk aversion it turns out that the optimal amount of money to invest in stocks is independent of wealth. The optimal consumption strategy is given as a deterministic bangbang strategy. In order to have a more realistic model we allow the risk aversion to be time and state dependent. Of special interest is the case were the risk aversion is inversely proportional to present wealth plus the financial value of future labor income net of consumption. Using the verification theorem we give a detailed analysis of this problem. It turns out that the optimal amount of money to invest in stocks is given by a linear function of wealth plus the financial value of future labor income net of consumption. The optimal consumption strategy is again given as amore »
 Authors:

^{[1]};
^{[2]}
 ATP (Danish Labour Market Supplementary Pension Scheme) (Denmark)
 University of Copenhagen, Department of Mathematical Sciences (Denmark)
 Publication Date:
 OSTI Identifier:
 22469914
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Applied Mathematics and Optimization; Journal Volume: 71; Journal Issue: 3; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springerny.com; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; DYNAMIC PROGRAMMING; EMPLOYMENT; FUNCTIONS; INCOME; INVESTMENT; MANPOWER; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERSONNEL; VERIFICATION