2018/05/03 by Constantinos Kardaras, Johannes Ruf, Kardaras, Constantinos +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.1805.01404
Let X and Y denote two independent squared Bessel processes of dimension m and n-m, respectively, with n≥ 2 and m ∈ [0, n), making X+Y a squared Bessel process of dimension n. For appropriately chosen function s, the process s (X+Y) is a local martingale. We study the representation and the dynamics of s(X+Y), projected on the filtration generated by X. This projection is a strict supermartingale if, and only if, m<2. The finite-variation term in its Doob-Meyer decomposition only charges the support of the Markov local time of X at zero.