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Project C3: Recursive utility with intertemporal substitution and related stochastic representation problems



Summary:

Intertemporal utility functions form the basic building block for dynamic economic models. We formulate a general theory of stochastic differential utility for intertemporal utility functions allowing for substitution and memory in robust settings. On the mathematical side, we study the existence of such utility functionals in the framework of G-backward stochastic differential equation (BSDE) theory. On the economic side, we will explore the consequences for optimal consumption and portfolio choice and aim to derive consumption--based asset pricing theories. Consumption occurs in many different goods and quality levels. In collaboration with research area B, we use the theory of stochastic partial differential equations to develop a theory of recursive utility for complex commodities whose characteristics may change over time.




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