Related papers: Dynamic Approaches for Some Time Inconsistent Prob…
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization…
Since Peng (1993) established a local maximum principle for a general stochastic control problem governed by forward-backward stochastic differential equations (FBSDEs), the corresponding partial differential equation (PDE) characterization…
We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…
We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
In this paper we study a generalization of the continuous time Principal-Agent problem allowing for time inconsistent utility functions, for instance of mean-variance type. Using recent results on the Pontryagin maximum principle for FBSDEs…
Dual control denotes a class of control problems where the parameters governing the system are imperfectly known. The challenge is to find the optimal balance between probing, i.e. exciting the system to understand it more, and caution,…
In this paper, we study the relationship between general maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems, where the control domain is not necessarily convex. The original problem is…
We extend the proof of the dynamic programming principle (DPP) for standard stochastic optimal control problems driven by general L\'{e}vy noises. Under appropriate assumptions, it is shown that the DPP still holds when the state process…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intra-personal…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a $d$-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of…
We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…
Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any stochastic primitives from some…
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…