This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the Gerber–Shiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cramér–Lundberg model) but also more general Lévy insurance risk...
This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating th...
This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks.
The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree...
This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin ...
This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed...
This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample...
This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in...
This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical...
This book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book begins with a brief discussion of basic notions and results from decision theory such as admissibility, minimaxity, and (generalized) Bayes estimation. It also presents Stein's unbiased risk estimator and the James-Stein estimator in the first chapter. In the following chapters, the authors consider estimation of the mean vector of a multivariate normal distribution in the known and unknown scale case when the covariance matrix is a multiple of the...
This book provides a self-contained introduction of Stein/shrinkage estimation for the mean vector of a multivariate normal distribution. The book beg...
This book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic differential equations (SDEs) as well as numerical methods for computing parabolic partial differential equations (PDEs). Particularly, Malliavin s integration by parts is effectively applied to the computation schemes combined with deep learning methods. Constructions of asymptotic expansion and weak approximation are given in detail with the theoretical convergence analysis. The schemes enable efficient computation for high-dimensional SDEs and fast...
This book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic different...
