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The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
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…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
Optimized trade execution is to sell (or buy) a given amount of assets in a given time with the lowest possible trading cost. Recently, reinforcement learning (RL) has been applied to optimized trade execution to learn smarter policies from…
Financial markets change their behaviours abruptly. The mean, variance and correlation patterns of stocks can vary dramatically, triggered by fundamental changes in macroeconomic variables, policies or regulations. A trader needs to adapt…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading…
This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by…
We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three…
We study optimal execution in markets with transient price impact in a competitive setting with $N$ traders. Motivated by prior negative results on the existence of pure Nash equilibria, we consider randomized strategies for the traders and…
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
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 explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and…
We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…
This paper studies the problem of maximizing expected utility from terminal wealth combining a static position in derivative securities, which we assume can be traded only at time zero, with a traditional dynamic trading strategy in stocks.…
In the context of investment analysis, we formulate an abstract online computing problem called a planning game and develop general tools for solving such a game. We then use the tools to investigate a practical buy-and-hold trading problem…