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

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  • Fabio Trojani

    ()

  • Roberto G. Ferretti

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.

Suggested Citation

  • Fabio Trojani & Roberto G. Ferretti, 2005. "General Analytical Solutions For Mertons'S-Type Consumption-Investment Problems," University of St. Gallen Department of Economics working paper series 2005 2005-02, Department of Economics, University of St. Gallen.
  • Handle: RePEc:usg:dp2005:2005-02
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    File URL: http://ux-tauri.unisg.ch/RePEc/usg/dp2005/DP-02_Tr.pdf
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    References listed on IDEAS

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    1. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    2. Fabio Trojani & Paolo Vanini, 2004. "Robustness and Ambiguity Aversion in General Equilibrium," Review of Finance, European Finance Association, vol. 8(2), pages 279-324.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    5. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    6. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Hamilton-Jacobi-Bellman equations; Higher Order Asymptotic Poli- cies; Merton's Model; Partial Equilibrium; Perturbation Theory;

    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

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