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We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
We consider the problem of dynamic pricing with limited supply. A seller has $k$ identical items for sale and is facing $n$ potential buyers ("agents") that are arriving sequentially. Each agent is interested in buying one item. Each…
We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed…
We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…
We consider an exchange who wishes to set suitable make-take fees to attract liquidity on its platform. Using a principal-agent approach, we are able to describe in quasi-explicit form the optimal contract to propose to a market maker. This…
We study the problem of option pricing and hedging strategies within the frame-work of risk-return arguments. An economic agent is described by a utility function that depends on profit (an expected value) and risk (a variance). In the…
We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…
We solve explicitly the Almgren-Chriss optimal liquidation problem where the stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and to use functional analysis tools. We show that this…
We study an optimal allocation problem for a system of independent Brownian agents whose states evolve under a limited shared control. At each time, a unit of resource can be divided and allocated across components to increase their drifts,…
We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous…
We consider a profit maximization problem in an urban mobility on-demand service, of which the operator owns a fleet, provides both exclusive and shared trip services, and dynamically determines prices of offers. With knowledge of the…
We study a portfolio selection problem in a continuous-time It\^o-Markov additive market with prices of financial assets described by Markov additive processes which combine L\'evy processes and regime switching models. Thus the model takes…
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…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise…
Simultaneous ascending auctions present agents with the exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. Auction theory provides little guidance for dealing with this…
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 show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that…