A Variational Analysis Approach to Solving the Merton Problem

Ali Al-Aradi and Sebastian Jaimungal

Papers from arXiv.org

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.

Date: 2020-03
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2003.08450

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