2023/06/05 by Ofelia Bonesini, Giorgia Callegaro, Bonesini, Ofelia +5
Economics, Econometrics and Finance · Social Sciences · #60G22 #65C20 #91G60 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.02708
openalex publication_date 2023/06/05 · openalex created_date 2023/06/07 · openalex updated_date 2026/08/02
We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go back, i.e., the transformation is reversible. We discuss existence and path-wise regularity of solutions for our class of stochastic differential equations. In the fractional kernel case, when H ∈ (0,\frac12), where H is the Hurst coefficient, we propose a numerical simulation scheme which exhibits a remarkable strong convergence rate of order 1/2, which constitutes a bold improvement when compared with the performance of available Euler schemes, whose strong rate of convergence is H.