2017/07/17 by Leão, Dorival, Ohashi, Alberto, Russo, Francesco
#Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1707.05234
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct ε-optimal stopping times and optimal values in full generality. Explicit rates of convergence are presented for optimal values based on reward functionals of path-dependent SDEs driven by fractional Brownian motion. In particular, the methodology allows us to design concrete Monte-Carlo schemes for non-Markovian optimal stopping time problems as demonstrated in the companion paper by Bezerra, Ohashi and Russo.