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 -