Related papers: Optimal Equilibria for Time-Inconsistent Stopping …
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
In optimal stopping problems, a Markov structure guarantees Markovian optimal stopping times (first exit times). Surprisingly, there is no analogous result for Markovian stopping games once randomization is required. This paper addresses…
We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on…
This paper studies a continuous-time portfolio selection problem under a general distribution of random risk aversion (RRA). We provide a complete characterization of all deterministic equilibrium strategies in closed form. Our results show…
This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion…
We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
The optimal \(H_{\infty}\) control problem over an infinite time horizon, which incorporates a performance function with a discount factor \(e^{-\alpha t}\) (\(\alpha > 0\)), is important in various fields. Solving this optimal…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
In this paper we study a general optimal liquidation problem with a control-dependent stopping time which is the first time the stock holding becomes zero or a fixed terminal time, whichever comes first. We prove a stochastic maximum…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We…
This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
We study L 1 -optimal stabilization of linear systems with finite and infinite horizons. Main results concern the existence, uniqueness and structure of optimal solutions, and the robustness of optimal cost.