2025/03/06 by Eduardo Abi Jaber, Alessandro Bondi, Jaber, Eduardo Abi +7 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #60H30 #91G80 #93E20 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2503.04323
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay.