Related papers: Optimal Trading with a Trailing Stop
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
We describe the solution of an optimal stopping problem for a stable L\'evy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…
We consider learning a trading agent acting on behalf of the treasury of a firm earning revenue in a foreign currency (FC) and incurring expenses in the home currency (HC). The goal of the agent is to maximize the expected HC at the end of…
To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a…
Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction…
In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional…
We investigate brokerage between traders from an online learning perspective. At any round $t$, two traders arrive with their private valuations, and the broker proposes a trading price. Unlike other bilateral trade problems already studied…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
We consider a controlled double-ended queue consisting of two classes of customers, labeled sellers and buyers. The sellers and buyers arrive in a trading market according to two independent renewal processes. Whenever there is a seller and…
An agent holds a position in a perpetual contract with payoff function $\psi$ and attempts to liquidate the position while managing transaction costs, inventory risk, and funding rate payments. By solving the agent's stochastic control…
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the…
This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential…
This study investigates an optimal consumption--investment problem in which the unobserved stock trend is modulated by a hidden Markov chain that represents different economic regimes. In the classical approach, the hidden state is…
Optimal execution is a sequential decision-making problem for cost-saving in algorithmic trading. Studies have found that reinforcement learning (RL) can help decide the order-splitting sizes. However, a problem remains unsolved: how to…