Related papers: Liquidation in Limit Order Books with Controlled I…

This paper studies the risk-adjusted optimal timing to liquidate an option at the prevailing market price. In addition to maximizing the expected discounted return from option sale, we incorporate a path-dependent risk penalty based on…

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…

We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial…

We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the…

We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, by using a limit order or a market order. For a diffusive market, we characterize the optimal limit order…

We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability…

We propose a static equilibrium model for limit order book where profit-maximizing investors receive an information signal regarding the liquidation value of the asset and execute via a competitive dealer with random initial inventory, who…

This paper studies the fill probabilities of limit orders placed at different price levels in a limit order book. These probabilities play a central role in execution optimization, as limit orders are not guaranteed to be executed and…

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for…

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…

We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). In this context, the limit orders, market orders, and cancel orders arrivals in the LOB are…

We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject…

An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…

We study a multi-dimensional optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience. In our model the value function can be described by a multi-dimensional backward…

In this paper, we analyze the optimal management of local memory systems, using the tools of stationary point processes. We provide a rigorous setting of the problem, building upon recent work, and characterize the optimal causal policy…

We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…

We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time.…

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity…

Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the…