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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.14059 |
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Table of Contents:
- The dynamic concave utility (or the dynamic convex risk measure) of an unbounded endowment is studied and represented as the value process in the unique solution of a backward stochastic differential equation (BSDE) with an unbounded terminal value, with the help of our recent existence and uniqueness results on unbounded solutions of scalar BSDEs whose generators have a linear, super-linear, sub-quadratic or quadratic growth. Moreover, the infimum in the dynamic concave utility is proved to be attainable. The Fenchel-Legendre transform (dual representation) of convex functions, the de la Vallée-Poussin theorem, and Young's and Gronwall's inequalities constitute the main ingredients of the dual representation.