A robust time‐inconsistent linear‐quadratic problem

2021 ◽  
Vol 31 (7) ◽  
pp. 2737-2761
Author(s):  
Binbin Si ◽  
Yuan‐Hua Ni ◽  
Qinglin Sun ◽  
Zengqiang Chen
Keyword(s):  
Linear Quadratic ◽  
Quadratic Problem ◽  
Time Inconsistent

Mixed Equilibrium Solution of Time-Inconsistent Stochastic Linear-Quadratic Problem

2019 ◽  
Vol 57 (1) ◽  
pp. 533-569 ◽  
Author(s):  
Yuan-Hua Ni ◽  
Xun Li ◽  
Ji-Feng Zhang ◽  
Miroslav Krstic
Keyword(s):  
Equilibrium Solution ◽  
Linear Quadratic ◽  
Quadratic Problem ◽  
Mixed Equilibrium ◽  
Time Inconsistent

Linear–Quadratic Time-Inconsistent Mean Field Games

2013 ◽  
Vol 3 (4) ◽  
pp. 537-552 ◽  
Author(s):  
A. Bensoussan ◽  
K. C. J. Sung ◽  
S. C. P. Yam
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Linear Quadratic ◽  
Time Inconsistent

scholarly journals On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

2014 ◽  
Vol 24 (4) ◽  
pp. 723-733
Author(s):  
K.Maciej Przyłuski
Keyword(s):  
Minimum Energy ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Minimum Norm Solution ◽  
Quadratic Problem ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Characterization of stochastic equilibrium controls by the Malliavin calculus

2021 ◽  
pp. 2150054
Author(s):  
Jiang Yu Nguwi ◽  
Nicolas Privault
Keyword(s):  
Malliavin Calculus ◽  
Linear Quadratic ◽  
Merton Problem ◽  
Classical Duality ◽  
The Mean ◽  
Time Inconsistent ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Quadratic Case

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.

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