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

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Optimal control of an objective functional with non-linearity between the conditional expectations : solutions to a class of time-inconsistent portfolio problems. / Kryger, Esben; Nordfang, Maj Britt; Steffensen, Mogens.

In: Mathematical Methods of Operations Research, Vol. 91, No. 3, 01.06.2020, p. 405-438.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kryger, E, Nordfang, MB & Steffensen, M 2020, 'Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems', Mathematical Methods of Operations Research, vol. 91, no. 3, pp. 405-438. https://doi.org/10.1007/s00186-019-00687-5

APA

Kryger, E., Nordfang, M. B., & Steffensen, M. (2020). Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems. Mathematical Methods of Operations Research, 91(3), 405-438. https://doi.org/10.1007/s00186-019-00687-5

Vancouver

Kryger E, Nordfang MB, Steffensen M. Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems. Mathematical Methods of Operations Research. 2020 Jun 1;91(3):405-438. https://doi.org/10.1007/s00186-019-00687-5

Author

Kryger, Esben ; Nordfang, Maj Britt ; Steffensen, Mogens. / Optimal control of an objective functional with non-linearity between the conditional expectations : solutions to a class of time-inconsistent portfolio problems. In: Mathematical Methods of Operations Research. 2020 ; Vol. 91, No. 3. pp. 405-438.

Bibtex

@article{9d36ac86de3842e5869e3dd393af0278,
title = "Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems",
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 = "Equilibrium control laws, Optimal control, Quadratic portfolio problems, Time-inconsistency",
author = "Esben Kryger and Nordfang, {Maj Britt} and Mogens Steffensen",
year = "2020",
month = jun,
day = "1",
doi = "10.1007/s00186-019-00687-5",
language = "English",
volume = "91",
pages = "405--438",
journal = "Mathematical Methods of Operations Research",
issn = "1432-2994",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Optimal control of an objective functional with non-linearity between the conditional expectations

T2 - solutions to a class of time-inconsistent portfolio problems

AU - Kryger, Esben

AU - Nordfang, Maj Britt

AU - Steffensen, Mogens

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - Equilibrium control laws

KW - Optimal control

KW - Quadratic portfolio problems

KW - Time-inconsistency

UR - http://www.scopus.com/inward/record.url?scp=85076581316&partnerID=8YFLogxK

U2 - 10.1007/s00186-019-00687-5

DO - 10.1007/s00186-019-00687-5

M3 - Journal article

AN - SCOPUS:85076581316

VL - 91

SP - 405

EP - 438

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 3

ER -

ID: 258767513