Singular recursive utility

We introduce the concept of singular recursive utility. This leads to a kind of singular backward stochastic differential equation (BSDE) which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Fu...

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2017-10, Vol.89 (6-7), p.994-1014
Main Authors: Dahl, K. R., Øksendal, B.
Format: Article
Language:English
Subjects:
Differential equations
generalized Skorohod reflection problem
optimal consumption
optimal control problem
Optimization
Reflection
singular backward stochastic differential equation
singular jump-diffusion processes
Singular recursive utility
stochastic maximum principle
Uniqueness
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Summary:We introduce the concept of singular recursive utility. This leads to a kind of singular backward stochastic differential equation (BSDE) which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular recursive utility. We derive sufficient and necessary maximum principles for this problem, and connect it to the Skorohod reflection problem. Finally, we apply our results to a specific cash flow. In this case, we find that the optimal consumption rate is given by the solution to the corresponding Skorohod reflection problem.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2017.1303067