Statistical Inference in Financial and Insurance Mathematics with R

Finance and insurance companies are facing a wide range of mathematical problems. Statistical experiments with independent and identically distributed sample are relatively common in the mentioned applications. Such classical experiments are now well understood including those with some exponential family of probability measures. But finance and insurance applications are also offering non-classical statistical experiments. Two examples will be treated within this book. On the one hand, the Generalized Linear Models (GLM) extends to non-Gaussian samples the standard regression method. On the other hand, the homogeneous Markov chains are considered. They appear naturally observing the price of an asset considered as the solution of some stochastic differential equation. In this monograph, special attention is paid to the notion of asymptotical efficiency in order to give the proper notion of estimation risk. Moreover, computations with the software R are provided. Presents the LAN (local asymptotic normality) property of likelihoods Combines the proofs of LAN property for different statistical experiments that appears in financial and insurance mathematics Provides the proper description of such statistical experiments and invites you to seek optimal estimators (performed in R) for such statistical experiments