Related papers: Optimal Trading with Linear and (small) Non-Linear…
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process,…
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…
For the stochastic multi-armed bandit (MAB) problem from a constrained model that generalizes the classical one, we show that an asymptotic optimality is achievable by a simple strategy extended from the $\epsilon_t$-greedy strategy. We…
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their…
We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short…
We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed…
We consider a retailer who buys energy in the wholesale market and resells it to final consumers. The retailer has to decide when to intervene to change the price he asks to his customers, in order to maximize his income. We model the…
We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon $T$. A trader uses both limit and market orders, and a…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
In this paper, we consider the adaptive linear quadratic Gaussian control problem, where both the linear transformation matrix of the state $A$ and the control gain matrix $B$ are unknown. The proposed adaptive optimal control only assumes…
In this work, we study economic model predictive control (MPC) in situations where the optimal operating behavior is periodic. In such a setting, the performance of a standard economic MPC scheme without terminal conditions can generally be…
We consider scalar decentralized average-cost infinite-horizon LQG problems with two controllers, focusing on the fast dynamics case when the (scalar) eigenvalue of the system is large. It is shown that the best linear controllers'…
We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we…
This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from [17], the cost functionals do not have…