BSDEs driven by time-changed Lévy noises and optimal control |
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Authors: | Giulia Di Nunno Steffen Sjursen |
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Affiliation: | 1. Center of Mathematics for Applications, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway;2. Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway |
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Abstract: | We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally appear in control problems. Here we prove a sufficient maximum principle for a general optimal control problem of a system driven by a time-changed Lévy noise. As an illustration we solve the mean–variance portfolio selection problem. |
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Keywords: | 60H10 91G80 |
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