We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the mul...We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.展开更多
文摘We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.
