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Erscheinungsjahr: 
2025
Quellenangabe: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 29 [Issue:] 3 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2025 [Pages:] 885-932
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
This article considers existence and uniqueness of infinite-horizon Epstein–Zin stochastic differential utility (EZ-SDU) for the case that the coefficients Rof relative risk aversion and Sof elasticity of intertemporal complementarity (the reciprocal of elasticity of intertemporal substitution) satisfy ϑ:=1−R1−S>1. In this sense, this paper is complementary to (Herdegen et al., Finance Stoch. 27, pp. 159–188). The main novelty of the case ϑ>1(as opposed to ϑ∈(0,1)) is that there is an infinite family of utility processes associated to every nonzero consumption stream. To deal with this issue, we introduce the economically motivated notion of a proper utility process, where, roughly speaking, a utility process is proper if it is nonzero whenever future consumption is nonzero. We proceed to show that for a very wide class of consumption streams C, there exists a proper utility process Vassociated to C. Furthermore, for a wide class of consumption streams C, the proper utility process Vis unique. Finally, we solve the optimal investment–consumption problem for an agent with preferences governed by EZ-SDU who invests in a constant-parameter Black–Scholes–Merton financial market and optimises over right-continuous consumption streams that have a unique proper utility process associated to them.
Schlagwörter: 
Epstein–Zin stochastic differential utility
Lifetime investment and consumption
Proper solutions
JEL: 
C61
G11
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