Integral representations of some functionals of fractional Brownian\n motion

2011/02/25 by Heikki Tikanmäki, Tikanmäki, Heikki
Economics, Econometrics and Finance · #60G22 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1102.5182

openalex publication_date 2011/02/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove change of variables formulas [It ^o formulas] for functions of both\narithmetic and geometric averages of geometric fractional Brownian motion. They\nare valid for all convex functions, not only for smooth ones. These change of\nvariables formulas provide us integral representations of functions of average\nin the sense of generalized Lebesgue-Stieltjes integral.\n

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