相关论文: Optimal stopping of Hunt and L\'evy processes

A functional representation of free L\'evy processes is established via an ensemble of unitarily invariant Hermitian matrix-valued L\'evy processes. This is accomplished by proving functional asymptotics of their empirical spectral…

A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is $C^1$ and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the…

Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an action that is the difference of a field…

We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…

We consider an infinite horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of…

In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…

This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random…

A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…

Decision processes with incomplete state feedback have been traditionally modeled as Partially Observable Markov Decision Processes. In this paper, we present an alternative formulation based on probabilistic regular languages. The proposed…

We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. [5] solved the case with i.i.d. hyperexponential jumps;…

This paper examines a class of singular stochastic control problems with convex objective functions. In Section 2, we use tools from convex analysis to derive necessary and sufficient first order conditions for this class of optimisation…

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…

We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional…

This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both…

Although maximum entropy method (maxEnt method) is currently the standard algorithm for extracting real frequency information from imaginary frequency Green function, still this method is beset with overfitting problem, which manifests…

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…

We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing…

In this paper we introduce a ten-parameter family of L\'{e}vy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and…

In Gapeev and K\"uhn (2005), the stochastic game corresponding to perpetual convertible bonds was considered when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but…

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting…