This paper studies an approximation method for the log likelihood function of a non-linear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently...

The purpose of this paper is to introduce the Gerber statistic, a robust co-movement measure for covariance matrix estimation for the purpose of portfolio construction. The Gerber statistic extends Kendall's Tau by counting the proportion of simultaneous co-movements in series when their...

The L1-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L1-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to...

Linear regression is widely-used in finance. While the standard method to obtain parameter estimates, Least Squares, has very appealing theoretical and numerical properties, obtained estimates are often unstable in the presence of extreme observations which are rather common in financial time...

We formulate a distributionally robust optimization problem where the deviation of the alternative distribution is controlled by a φ-divergence penalty in the objective, and show that a large class of these problems are essentially equivalent to a mean-variance problem. We also show that while...

We study the out-of-sample properties of robust empirical optimization problems with smooth φ-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative “robustness parameter” δ that controls the size of the deviations...

In this paper, we study the out-of-sample properties of robust empirical optimization and develop a theory for data-driven calibration of the “robustness parameter” for worst-case maximization problems with concave reward functions. Building on the intuition that robust optimization reduces...