Metric-Affine Myrzakulov Gravity Theories

In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître–Robertson–Walker background to study cosmological aspects and applications. Historical motivation for this research is thoroughly reviewed and specific physical motivations are provided for the aforementioned family of alternative theories of gravity.

Martingale Models for the Short Rate

This chapter is devoted to an overview and analysis of the most common short rate models, such as the Vasiček, Dothan, Hull–White, and CIR models. These models are analyzed and classified from the point of view of positive short rates, normal distribution, mean reversion, and computability. In particular we present the theory of affine term structures, and discuss the inversion of the yield curve. Analytical results for bond prices and bond options are presented for all the affine models.