Related papers: Stochastic Maximum Principle for Optimal Liquidati…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e.…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
This paper is concerned with devising the nonlinear optimal guidance for intercepting a stationary target with a fixed impact time. According to Pontryagin's Maximum Principle (PMP), some optimality conditions for the solutions of the…
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
This paper is concerned with an optimal stock selling rule under a Markov chain model. The objective is to find an optimal stopping time to sell the stock so as to maximize an expected return. Solutions to the associated variational…
In this article we derive a Pontryagin maximum principle (PMP) for discrete-time optimal control problems on matrix Lie groups. The PMP provides first order necessary conditions for optimality; these necessary conditions typically yield two…
In this work we provide explicit conditions on the existence of optimal feedback controls for stochastic processes with regime-switching. We use the compactification method which needs less regularity conditions on the coefficients of the…
A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
It is well known that stability is the most fundamental nature with regard to a control system, in view of this, the stabilization becomes an inevitable control problem. This article mainly discusses the optimal control and stabilization…
In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set…
We consider a stochastic transportation problem between two prescribed probability distributions (a source and a target) over processes with general drift dependence and with free end times. First, and in order to establish a dual…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
In this paper, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and…
Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) in [9] and the dynamic programming principle (DPP) in [10] for a fully coupled forward-backward stochastic controlled system (FBSCS)…
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent…
This paper investigates optimal control problems for delayed systems governed by Infinitely Anticipated Backward Stochastic Differential Equations (IABSDEs). Unlike existing frameworks limited to bounded delays, we introduce a generalized…