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Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases that are difficult to control. Motivated by a novel characterization of the CVA as the value of an option with an early exercise opportunity at a stochastic time, we provide an approximation for CVA and other credit charges that rely only on the sign of the regression functions. The values are determined, instead, by pathwise deflated cash flows. A comparison of CVA for Bermudan swaptions and cancellable swaps shows that the proposed approximation results in much smaller errors than the standard approach of using the regression function values.

In this paper, we investigate coefficient-based regularized least squares regression problem in a data dependent hypothesis space. The learning algorithm is implemented with samples drawn by unbounded sampling processes and the error analysis is performed by a stepping-stone technique. A new error decomposition technique is proposed for the error analysis. The regularization parameters in our setting provide much more flexibility and adaptivity. Sharp learning rates are addressed by means of l²-empirical covering numbers under a moment hypothesis condition.

Identification of individuals who are at risk for sudden cardiac death (SCD) remains a formidable challenge. T-wave alternans (TWA) evaluation is emerging as an important tool for risk stratification in patients with heart diseases. Several methods have been developed in recent years to detect and quantify TWA. One such method is known as the correlation method (CM). This method performs well for different levels of TWA and phase shifts in the time domain, but it is sensitive to noise and requires higher quality of electrocardiogram (ECG) signal for test. In this paper, we propose a modified correlation method (MCM) to ensure a robust and accuracy detection of TWA. Compared with CM, MCM add a stage of T-wave curve fitting before media T-wave template, and the TWA magnitude is obtained by meaning the maximum absolute difference between even and odd T-wave. Our assessment study demonstrates the improved performance of the proposed algorithm.

This paper is concerned with the approximation of data using linear models for which there is additional information to be incorporated into the analysis. This situation arises, for example, in Tikhonov regularisation, model averaging, Bayesian inference and approximation with Gaussian process models. In a least-squares approximation process, the m-vector of data y is approximated by a linear function ŷ = Hy of the data, where H is an m × m matrix related to the observation matrix. The effective number of degrees of freedom associated with the model is given by the sum of the eigenvalues of H. For standard linear least-squares regression, the matrix H is a projection and has n eigenvalues equal to 1 and all others zero, where n is the number of parameters in the model. Incorporating prior information about the parameters reduces the effective number of degrees of freedom since the ability of the model to approximate the data vector y is partially constrained by the prior information. We give a general approach for providing bounds on the effective number of degrees of freedom for models with prior information on the parameters and illustrate the approach on common problems. In particular, we show how the effective number of degrees of freedom depends on spatial or temporal correlation lengths associated with Gaussian processes. The correlation lengths are seen to be tuning parameters used to match the model degrees of freedom to the (generally unknown) number of degrees of freedom associated with the system giving rise to the data. We also show how Gaussian process models can be related to Tikhonov regularisation for an appropriate set of basis functions.