Related papers: Optimal Trading with Linear and (small) Non-Linear…
We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal…
The initial boundary value problem for a Cahn-Hilliard system subject to a dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary condition is the point of emphasis. By the…
In this paper we propose a mathematical framework to address the uncertainty emergingwhen the designer of a trading algorithm uses a threshold on a signal as a control. We rely ona theorem by Benveniste and Priouret to deduce our Inventory…
The goal of this work is to study binary market models with transaction costs, and to characterize their arbitrage opportunities. It has been already shown that the absence of arbitrage is related to the existence of \lambda-consistent…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact…
We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time.…
We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the…
In the paper we study markets with concave transaction costs which depend in a concave way on the volume of transaction. This is typical situation in the case of small investors, which commonly appears in currency and real estate markets.…
Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads…
We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…
We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for…
We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power…
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 consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
This paper develops a technique for computing a quadratic terminal cost for linear model predictive controllers that is valid for all states in the maximal control invariant set. This maximizes the set of recursively feasible states for the…
We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure…