GENERAL ANALYTICAL SOLUTIONS FOR MERTONS'S-TYPE CONSUMPTION-INVESTMENT PROBLEMS

Fabio Trojani (fabio.trojani@usi.ch) and Roberto G. Ferretti

University of St. Gallen Department of Economics working paper series 2005 from Department of Economics, University of St. Gallen

Abstract: We 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.

Keywords: Hamilton-Jacobi-Bellman equations; Higher Order Asymptotic Poli- cies; Merton's Model; Partial Equilibrium; Perturbation Theory (search for similar items in EconPapers)
JEL-codes: C60 C61 G11 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2005-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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