The G-Martingale Approach for G-Utility Maximization
2022
Online
report
In this paper, we study representative investor's G-utility maximization problem by G-martingale approach in the framework of G-expectation space proposed by Peng \cite{Pe19}. Financial market has only a bond and a stock with uncertainty characterized by G-Brownian motions. The routine idea of \cite{Wxz} fails because that the quadratic variation process of a G-Brownian motion is also a stochastic process. To overcome this difficulty, an extended nonlinear expectation should be pulled in. A sufficient condition of G-utility maximization is presented firstly. In the case of log-utility, an explicit solution of optimal strategy can be obtained by constructing and solving a couple of G-FBSDEs, then verifying the optimal strategy to meet the sufficient condition. As an application, an explicit solution of a stochastic interest model is obtained by the same approach. All economic meanings of optimal strategies are consistent with our intuitions.
Comment: 16pages
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The G-Martingale Approach for G-Utility Maximization
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Autor/in / Beteiligte Person: | Chen, Qiguan ; Song, Yulin ; Wang, Zengwu ; Yuan, Zengting |
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Veröffentlichung: | 2022 |
Medientyp: | report |
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