2013/06/18 by Wei Chen, Chen, Wei · 2 citations
Economics, Econometrics and Finance · #60E05 #60G18 #60G22 #60H40 #60K #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1306.4070
openalex publication_date 2013/06/18 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
G-framework is presented by Peng [41] for measure risk under uncertainty. In\nthis paper, we define fractional G-Brownian motion (fGBm). Fractional\nG-Brownian motion is a centered G-Gaussian process with zero mean and\nstationary increments in the sense of sub-linearity with Hurst index H\∈\n(0,1). This process has stationary increments, self-similarity, and long rang\ndependence properties in the sense of sub-linearity. These properties make the\nfractional G-Brownian motion a suitable driven process in mathematical finance.\nWe construct wavelet decomposition of the fGBm by wavelet with compactly\nsupport. We develop fractional G-white noise theory, define G-It o-Wick\nstochastic integral, establish the fractional G-It o formula and the\nfractional G-Clark-Ocone formula, and derive the G-Girsanov's Theorem. For\napplication the G-white noise theory, we consider the financial market modelled\nby G-Wick-It o type of SDE driven by fGBm. The financial asset price modelled\nby fGBm has volatility uncertainty, using G-Girsanov's Theorem and\nG-Clark-Ocone Theorem, we derive that sublinear expectation of the discounted\nEuropean contingent claim is the bid-ask price of the claim.\n