Related papers: Non-Markovian optimal stopping problems and constr…
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence…
We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a…
In this paper we look at ergodic BSDEs in the case where the forward dynamics are given by the solution to a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck SDE with L\'evy noise, taking values in a separable Hilbert space.…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
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…
We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework.…
We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the…
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used…
We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the…
In the first part of this paper, we study RBSDEs in the case where the filtration is not quasi-left continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal…
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…
In this paper, we consider the optimal stopping problem on semi-Markov processes (SMPs) with finite horizon, and aim to establish the existence and computation of optimal stopping times. To achieve the goal, we first develop the main…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution…
This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs for short) with an unbounded terminal condition. Our results are deeply linked…
This paper is devoted to solving a real valued backward stochastic differential equation with jumps where the time horizon may be finite or infinite. Under linear growth generator, we prove existence of a minimal solution. Using a…