Related papers: Optimal switching problem for marked point process…
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method.…
We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set…
This article deals with the starting and stopping problem under Knightian uncertainty, i.e., roughly speaking, when the probability under which the future evolves is not exactly known. We show that the lower price of a plant submitted to…
We consider a robust impulse control problem in finite horizon where the underlying uncertainty stems from an impulsively and continuously controlled functional stochastic differential equation (FSDE) driven by Brownian motion. We assume…
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 consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…
We propose a recursive algorithm for the numerical computation of the optimal value function $\inf_{t\le\tau\le T} E \Big[\sup_{0\le s\le T } Y_s / Y_{\tau} \big| {\cal F}_t\Big]$ over the stopping times $\tau$ with respect to the…
In this paper, we study the optimal multiple stopping problem under Knightian uncertainty both under discrete-time case and continuous-time case. The Knightian uncertainty is modeled by a single real-valued function g, which is the…
We consider the optimal stopping problem with non-linear $f$-expectation (induced by a BSDE) without making any regularity assumptions on the reward process $\xi$. and with general filtration. We show that the value family can be aggregated…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium"…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
This paper is concerned with one kind of partially observed progressive optimal control problems of coupled forward-backward stochastic systems driven by both Brownian motion and Poisson random measure with risk-sensitive criteria. The…
We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this…
This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in…
In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…
In this paper we formulate and study an optimal switching problem under partial information. In our model the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…