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General Analytical Solutions For Mertons'S-Type Consumption-Investment Problems

  • Fabio Trojani

    ()

  • Roberto G. Ferretti

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.

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File URL: http://www1.vwa.unisg.ch/RePEc/usg/dp2005/DP-02_Tr.pdf
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Paper 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.

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Length: 41 pages
Date of creation: Jan 2005
Date of revision:
Handle: RePEc:usg:dp2005:2005-02
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  1. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000. "A Monte-Carlo Method for Optimal Portfolios," CIRANO Working Papers 2000s-05, CIRANO.
  2. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  3. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  4. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Fabio Trojani & Paolo Vanini, 2004. "Robustness and Ambiguity Aversion in General Equilibrium," Review of Finance, Springer, vol. 8(2), pages 279-324.
  6. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
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