Faculty of Economics and Business Administration Publications Database

Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets

Seifried, Frank Thomas
Steffensen, Mogens
Volume: 17
Number: 1
Pages: 161 - 196
Month: January
ISSN-Print: 0949-2984
Link External Source: Online Version
Year: 2013
Keywords: Consumption portfolio optimization; Recursive utility; Stochastic control approach; Stochastic volatility; Unspanned state process; Campbell Shiller approximation
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.