Consumption-portfolio optimization with recursive utility in incomplete markets

Holger Kraft (), Frank Seifried () and Mogens Steffensen ()

Finance and Stochastics, 2013, vol. 17, issue 1, 196 pages

Abstract: In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein–Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton–Jacobi–Bellman equation and provide a suitable verification theorem. The proof of this verification theorem is complicated by the fact that the Epstein–Zin aggregator is non-Lipschitz, so standard verification results (e.g. in Duffie and Epstein, Econometrica 60, 393–394, 1992 ) are not applicable. We provide new explicit solutions to the Bellman equation with Epstein–Zin preferences in an incomplete market for non-unit elasticity of intertemporal substitution (EIS) and apply our verification result to prove that they solve the consumption-investment problem. We also compare our exact solutions to the Campbell–Shiller approximation and assess its accuracy. Copyright Springer-Verlag 2013

Keywords: Consumption-portfolio optimization; Recursive utility; Stochastic control approach; Stochastic volatility; Unspanned state process; Campbell–Shiller approximation; 93E20; 91G10; G11; D91; C61 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (34)

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DOI: 10.1007/s00780-012-0184-1

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