Related papers: Liquidation in Limit Order Books with Controlled I…
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional…
In this paper, we consider controlled linear dynamical systems in which the controller has only access to a compressed version of the system state. The technical problem we investigate is that of allocating compression resources over time…
In this paper, we study the long time behavior of an optimal liquidation problem with semimartingale strategies and external flows. To investigate the limit rigorously, we study the convergence of three BSDEs characterizing the value…
The scope of this paper is to study the optimal stopping problems associated to a stochastic process, which may represent the gain of an investment, for which information on the final value is available a priori. This information may…
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
Inventory and queueing systems are often designed by controlling weighted combination of some time-averaged performance metrics (like cumulative holding, shortage, server-utilization or congestion costs); but real-world constraints, like…
We introduce a model for limit order book of a certain security with two main features: First, both the limit orders and market orders for the given asset are allowed to appear and interact with each other. Second, the high frequency…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
In this article, we develop a general framework to study optimal execution and to price block trades. We prove existence of optimal liquidation strategies and we provide regularity results for optimal strategies under very general…
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently…