Computational Economics

, Volume 49, Issue 1, pp 17–65 | Cite as

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



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.


Pessimistic agents Time-discounting Linear exponential quadratic Gaussian 

JEL Classification




I wish to thank Fausto di Biase and seminar participants at LUISS University, the University of Bologna, the University of Tor Vergata, the EIEF Center in Rome, and the 2014 John Cabot University Economic Theory Workshop


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Pescara, Università Gabriele d’AnnunzioPescaraItaly

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