2024/05/10 by Carlos Escudero, Escudero, C., Fernando Maccari Lara +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2405.06854
openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 generalizes previous results that used convexity, and also guarantees the robustness against arbitrage of so-designed automatic market makers. The theoretical results are illustrated by families of examples given by generalized means, and also by numerical simulations in certain concrete cases. These simulations along with the mathematical analysis suggest that the quasilinear-trade-function based automatic market makers might replicate the functioning of those based on convex functions, in particular regarding their resilience to arbitrage.