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A Variational Analysis Approach to Solving the Merton Problem

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  • Ali Al-Aradi
  • Sebastian Jaimungal

Abstract

We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization of the optimal portfolio for general utility functions in terms of a forward-backward stochastic differential equation (FBSDE) and derive solutions for a number of well-known utility functions. Our results complement a previous studies conducted on optimal strategies in markets driven by Brownian noise with random drift and volatility parameters.

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  • Ali Al-Aradi & Sebastian Jaimungal, 2020. "A Variational Analysis Approach to Solving the Merton Problem," Papers 2003.08450, arXiv.org.
    • Handle: RePEc:arx:papers:2003.08450
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    References listed on IDEAS

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    1. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.
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    6. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(3), pages 268-294, May.
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    14. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
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