Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets
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Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets. / Kraft, Holger; Seifried, Frank Thomas ; Steffensen, Mogens.
In: Finance and Stochastics, Vol. 17, 2013, p. 161-196.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets
AU - Kraft, Holger
AU - Seifried, Frank Thomas
AU - Steffensen, Mogens
PY - 2013
Y1 - 2013
N2 - 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 ofthis 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.
AB - 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 ofthis 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.
U2 - 10.1007/s00780-012-0184-1
DO - 10.1007/s00780-012-0184-1
M3 - Journal article
VL - 17
SP - 161
EP - 196
JO - Finance and Stochastics
JF - Finance and Stochastics
SN - 0949-2984
ER -
ID: 102779312