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Time-consistent investment and consumption strategies under a general discount function

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In the present paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting, a context that gives rise to time-inconsistency of the decision-maker. We consider equilibrium policies within the class of open-loop controls that are characterized, in our context, by means of a variational method which leads to a stochastic system that consists of a flow of forward-backward stochastic differential equations and an equilibrium condition. An explicit representation of the equilibrium policies is provided for the special cases of power, logarithmic and exponential utility functions.

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Journal of Risk and Financial Management, 2021, vol. 14, num. 2

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Time-consistent investment and consumption strategies under a general discount function