General Analytical Solutions For Mertons'S-Type Consumption-Investment Problems
AbstractWe solve analytically the Merton's problem of an investor with time additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We characterize all terms in the power series by a recursive formula, allowing analytical computations to arbitrary order. Some applications to explicit model settings highlight a very satisfactory accuracy of finite order approximations provided by our power series solution approach.
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Bibliographic InfoPaper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2005 with number 2005-02.
Length: 41 pages
Date of creation: Jan 2005
Date of revision:
Hamilton-Jacobi-Bellman equations; Higher Order Asymptotic Poli- cies; Merton's Model; Partial Equilibrium; Perturbation Theory;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-05-29 (All new papers)
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