Optimal sampling for density estimation in continuous time

Optimal importance sampling with explicit formulas in continuous time

In the Black-Scholes model, consider the problem of selecting a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options. Employing Large Deviations techniques, the asymptotically optimal change of drift is identified as the solution to a one-dimensional variational problem, which may be reduced to the associated Euler-Lagrange differential equ...

Optimal Sampling for Parameters Estimation

In the problems concerning prediction and modeling, parameters estimation constitutes one of the main uncertain items that must be taken into account. The easiest way to minimize this uncertainty is to collect great amounts of data. The aim of this work is to build a decision model able to choose the optimal position of the sample point used for the parameters estimation, minimizing the paramet...

Continuous Iterated Density Estimation

Sample-Optimal Density Estimation in Nearly-Linear Time

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let f be the density function of an arbitrary univariate distribution, and suppose that f is OPT close in L1-distance to an unknown piecewise polynomial function with t interval pieces and degree d. Our algorithm draws n = O(t(d+...

Optimal Iv Identification and Estimation of Continuous-time Tf Models

The paper outlines an optimal, maximum likelihood formulation of the continuoustime transfer function estimation problem and shows how the Refined Instrumental Variable (RIVC) algorithm provides an iterative solution to this problem. With the help of a simulation example, it then compares and contrasts the performance of the RIVC algorithm with that of two other, sub-optimal, continuous-time tr...