Related papers: Fredholm Approach to Nonlinear Propagator Models
Optimal execution of portfolio transactions is the essential part of algorithmic trading. In this paper we present in simple analytical form the optimal trajectory for risk-averse trader with the assumption of exponential market recovery…
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a…
We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption,…
We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can…
We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas…
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…
In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order,…
The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We prove that…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional…
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift…
Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient…
In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival…
In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight…
We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon…
In this paper, we introduce a novel reinforcement learning framework for optimal trade execution in a limit order book. We formulate the trade execution problem as a dynamic allocation task whose objective is the optimal placement of market…
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully…
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 which both order book depth and resilience evolve randomly in time. Trading is allowed in both…