TY - THES
A1 - Seiferling, Thomas
T1 - Recursive Utility and Stochastic Differential Utility: From Discrete to Continuous Time
N2 - In this thesis, mathematical research questions related to recursive utility and stochastic differential utility (SDU) are explored.
First, a class of backward equations under nonlinear expectations is investigated: Existence and uniqueness of solutions are established, and the issues of stability and discrete-time approximation are addressed. It is then shown that backward equations of this class naturally appear as a continuous-time limit in the context of recursive utility with nonlinear expectations.
Then, the Epstein-Zin parametrization of SDU is studied. The focus is on specifications with both relative risk aversion and elasitcity of intertemporal substitution greater that one. A concave utility functional is constructed and a utility gradient inequality is established.
Finally, consumption-portfolio problems with recursive preferences and unspanned risk are investigated. The investor's optimal strategies are characterized by a specific semilinear partial differential equation. The solution of this equation is constructed by a fixed point argument, and a corresponding efficient and accurate method to calculate optimal strategies numerically is given.
Y1 - 2016
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4380
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-43808
ER -