H–J–B Equations of Optimal Consumption-Investment and Verification Theorems

Journal Article · Wed Apr 15 00:00:00 EDT 2015 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-014-9258-0· OSTI ID:22469995

Nagai, Hideo ^[1]

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1. Kansai University, Department of Mathematics, Faculty of Engineering Science (Japan)

We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.

• OSTI ID: 22469995
• Journal Information: Applied Mathematics and Optimization, Vol. 71, Issue 2; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSUMPTION RATES
DYNAMIC PROGRAMMING
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
VERIFICATION