Related papers: Optimal switching problem for marked point process…
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…
In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent.…
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…
This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation.…
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive…
We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
We obtain existence and uniqueness in L^p, p>1 of the solutions of a backward stochastic differential equations (BSDEs for short) driven by a marked point process, on a bounded interval. We show that the solution of the BSDE can be…
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…
This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version…
We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichlet form and with measure data. We give a stochastic…
We study a discrete time approximation scheme for the solution of a doubly reflected Backward Stochastic Differential Equation (DBBSDE in short) with jumps, driven by a Brownian motion and an independent compensated Poisson process.…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…
In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle…
The multiple disorder problem seeks to determine a sequence of stopping times which are as close as possible to the unknown times of disorders at which the observation process changes its probability characteristics. We derive closed form…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its…