Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2014/3: Recursive utility using the stochastic maximum principle

Knut K. Aase ()
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Knut K. Aase: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous time model. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. With existence granted, the market portfolio is determined in terms of future utility and aggregate consumption in equilibrium. The equilibrium real interest rate is also derived, and the the model is shown to be consistent with reasonable values of the parameters of the utility function when calibrated to market data, under various assumptions.

Keywords: The equity premium puzzle; the risk-free rate puzzle; recursive utility; the stochastic maximum principle

JEL-codes: D51; D53; D90; E21; G10; G12

35 pages, First version: February 20, 2014. Revised: March 25, 2015.

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