2017/10/16 by Yuki Hirai, Hirai, Yuki
Economics, Econometrics and Finance · #60H05 #60H99 #Economic theories and models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1710.05541
openalex publication_date 2017/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend some results about Föllmer's pathwise Itô calculus that have only been derived for continuous paths to càdlàg paths with quadratic variation. We study some fundamental properties of pathwise Itô integrals with respect to càdlàg integrators, especially associativity and the integration by parts formula. Moreover, we study integral equations with respect to pathwise Itô integrals. We prove that some classes of integral equations, which can be explicitly solved in the usual stochastic calculus, can also be solved within the framework of Föllmer's calculus.