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Pessimistic Optimal Choice for Risk-Averse Agents: The Continuous-Time Limit

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  • Paolo Vitale

    (University of Pescara, Università Gabriele d’Annunzio)

Abstract

We extend Hansen and Sargent’s (Discounted linear exponential quadratic gaussian control, 1994, IEEE Trans Autom Control 40:968–971 1995, 2013) analysis of dynamic optimization with risk-averse agents in two directions. Firstly, following Whittle (Risk-sensitive optimal control, 1990), we show that the optimal risk-averse policy is identified via a pessimistic choice mechanism and described by simple recursive formulae. Secondly, we investigate the continuous-time limit and show that sufficient conditions for the existence of optimal solutions coincide with those which apply under risk-neutrality. Our analysis is conducted both under perfect and imperfect state observation. As an illustrative example, we analyze the optimal production policy of an entrepreneur running a monopolistic firm which faces a demand schedule subject to stochastic shocks, showing that risk-aversion induces her to act more aggressively.

Suggested Citation

  • Paolo Vitale, 2017. "Pessimistic Optimal Choice for Risk-Averse Agents: The Continuous-Time Limit," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 17-65, January.
    • Handle: RePEc:kap:compec:v:49:y:2017:i:1:d:10.1007_s10614-015-9547-y
    DOI: 10.1007/s10614-015-9547-y
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    References listed on IDEAS

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    1. Vitale, Paolo, 2012. "Risk-averse insider trading in multi-asset sequential auction markets," Economics Letters, Elsevier, vol. 117(3), pages 673-675.
    2. van der Ploeg, Frederick, 2009. "Prudent monetary policy and prediction of the output gap," Journal of Macroeconomics, Elsevier, vol. 31(2), pages 217-230, June.
    3. Frederick Ploeg, 2010. "Political economy of prudent budgetary policy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 17(3), pages 295-314, June.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    5. Hong Zhang, 2004. "Dynamic Beta, Time-Varying Risk Premium, and Momentum," Yale School of Management Working Papers amz2637, Yale School of Management, revised 01 Mar 2005.
    6. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    7. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    8. Lars Peter Hansen & Thomas J. Sargent, 2013. "Recursive Models of Dynamic Linear Economies," Economics Books, Princeton University Press, edition 1, number 10141.
    9. Holden, Craig W. & Subrahmanyam, Avanidhar, 1994. "Risk aversion, imperfect competition, and long-lived information," Economics Letters, Elsevier, vol. 44(1-2), pages 181-190.
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    Cited by:

    1. Edilio Valentini & Paolo Vitale, 2022. "A Dynamic Oligopoly with Price Stickiness and Risk-Averse Agents," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 8(3), pages 697-718, November.
    2. Edilio Valentini & Paolo Vitale, 2019. "Optimal Climate Policy for a Pessimistic Social Planner," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(2), pages 411-443, February.
    3. Vitale, Paolo, 2018. "Robust trading for ambiguity-averse insiders," Journal of Banking & Finance, Elsevier, vol. 90(C), pages 113-130.
    4. Valentini, Edilio & Vitale, Paolo, 2019. "Uncertainty and Risk-aversion in a Dynamic Oligopoly with Sticky Prices," ETA: Economic Theory and Applications 285025, Fondazione Eni Enrico Mattei (FEEM).
    5. Vitale, Paolo, 2018. "Optimal monetary policy for a pessimistic central bank," Journal of Macroeconomics, Elsevier, vol. 58(C), pages 39-59.

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    More about this item

    Keywords

    Pessimistic agents; Time-discounting; Linear exponential quadratic Gaussian;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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