Description: In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo LSM approach proposed by Longstaff and Schwartz 2001 and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a continuous scale with just one tuning parameter. Numerical results on American put options indicate that we need to use more than a linear regression, but as the regression becomes more complex, the accuracy of the LSM method quickly deteriorates. From 39th Actuarial Research Conference.

Description: The purpose of this paper is to introduce the use of least squares for estimating parameters of mortality curves and discuss the advantages of this method.

Description: In this paper, we study a survival regression model known as Cox's proportional Hazards model. We assume that the data available are already grouped and develop a minimum distance estimation procedure that is also applicable when the data are also left or right censored. Asymptotic properties of the estimators are established and the numerical implementation of the method based on an iterated reweighted least squares algorithm is discussed.

Description: Users of statistical packages should be more aware of the influence that outlying data points can have on their statistical analyses. Robust procedures provide formal methods to spot these outliers and reduce their influence. While a few robust procedures are mentioned in this article, one is emphasized and it is motivated by maximum likelihood estimation to make it seem more natural. In this article, the author will try to provide some background, beginning with maximum likelihood estimation of one parameter, that will hopefully make robust estimation seem natural and rather easy.