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We present a novel method for solving a class of time-inconsistent optimal stopping problems by reducing them to a family of standard stochastic optimal control problems. In particular, we convert an optimal stopping problem with a…

In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…

We study a nonlinear system of partial differential equations arising in macroeconomics which utilizes a mean field approximation. This system together with the corresponding data, subject to two moment constraints, is a model for debt and…

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

In this paper we establish that the time-harmonic elasticity problem in a half-strip with non-homogeneous Dirichlet conditions on its boundary section and traction-free conditions on its upper and lower boundaries, has a unique weak…

In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our…

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…

We consider a class of time-inhomogeneous optimal stopping problems and we provide sufficient conditions on the data of the problem that guarantee monotonicity of the optimal stopping boundary. In our setting, time-inhomogeneity stems not…

Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all…

The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…

This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion…

We consider the optimal stopping problem consisting in, given a strong Markov process, a reward function and a discount rate, finding the stopping time such that the expected reward at the stopping time is maximum. The approach we follow,…

We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…

We consider time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean-field game theory, and describe Nash equilibria of games with a large number of agents aiming…

This is a companion paper of [Mixed equilibrium solution of time-inconsistent stochastic LQ problem, arXiv:1802.03032], where general theory has been established to characterize the open-loop equilibrium control, feedback equilibrium…

In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…

We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in…

This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of…

The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…

This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…