Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems

Esben Kryger (), Maj-Britt Nordfang () and Mogens Steffensen ()

Mathematical Methods of Operations Research, 2020, vol. 91, issue 3, No 2, 405-438

Abstract: Abstract We present a modified verification theorem for the equilibrium control of a general class of portfolio problems. The general class of portfolio problems studied in this paper, is characterized by an objective where the investor seeks to maximize a functional of two conditional expectations of terminal wealth. The objective functional is allowed to be non-linear in the conditional expectations, and thus the problem class is in general terms time-inconsistent. In addition, we provide a corrected proof of the verification theorem and apply the theorem to a number of quadratic, time-inconsistent portfolio problems and determine their solutions. Some of the quadratic portfolio problems have not previously been solved analytically.

Keywords: Time-inconsistency; Quadratic portfolio problems; Optimal control; Equilibrium control laws (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00186-019-00687-5

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