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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…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman…

This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…

This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often…

This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…

In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability…

We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading…

The present paper investigates how insiders strategically navigate ongoing legal risk while leveraging stealth trading within a continuous-time Kyle-type framework. Legal enforcement operates concurrently with trading, which dynamic can be…

This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single…

This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs…

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…

This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the…

Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant…

A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…

Stablecoins, which are primarily intended to function as a global reserve of value are insubstantial in their design and present many failure points. The primary mechanism to enable these coins to hold on to a fixed value is by backing them…

Continuum soft robots are inherently underactuated and subject to intrinsic input constraints, making dynamic control particularly challenging, especially in hybrid rigid-soft robots. While most existing methods focus on quasi-static…