2010/05/03 by Michel Fliess, Cédric Join, Fliess, Michel +1
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1005.0194
openalex publication_date 2010/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.