Related papers: Liquidation in Limit Order Books with Controlled I…
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This…
In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption…
We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share…
We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred…
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters…
This paper presents an optimal strategy for portfolio liquidation under discrete time conditions. We assume that N risky assets held will be liquidated according to the same time interval and order quantity, and the basic price processes of…
We provide an explicit characterization of the optimal market making strategy in a discrete-time Limit Order Book (LOB). In our model, the number of filled orders during each period depends linearly on the distance between the fundamental…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
We study the optimal liquidation problems in target zone models using dynamic programming methods. Such control problems allow for stochastic differential equations with reflections and random coefficients. The value function is…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the…
We introduce a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution, costs, and P&L. The book state is projected onto a tractable representation based on spread and volume…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space…
This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit…
The distribution of liquidity within the limit order book is essential for the impact of market orders on the stock price and the emergence of price shocks. Limit orders are characterized by stylized facts: The number of inserted limit…
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of…
This paper studies an open question in the warehouse problem where a merchant trading a commodity tries to find an optimal inventory-trading policy to decide on purchase and sale quantities during a fixed time horizon in order to maximize…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…