Related papers: Extension of Switch Point Algorithm to Boundary-Va…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
We establish the first general regularity result for constrained optimal control problems arising naturally in mathematical physics and mathematical biology. Namely, we prove that for a large class of problems of the form ``maximise $\int…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
We consider the problem of designing a sequential decision making agent to maximize an unknown time-varying function which switches with time. At each step, the agent receives an observation of the function's value at a point decided by the…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of…
We study the piecewise constant bandit problem where the expected reward is a piecewise constant function with one change point (discontinuity) across the action space $[0,1]$ and the learner's aim is to locate the change point. Under the…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
Inventory and queueing systems are often designed by controlling weighted combination of some time-averaged performance metrics (like cumulative holding, shortage, server-utilization or congestion costs); but real-world constraints, like…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition…
We consider the optimal control problem in a two-qubit system with bounded amplitude. Two cases are studied: quantum state preparation and entanglement creation. Cost functions, fidelity and concurrence, are optimized over bang-off controls…
The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established.…
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the…