In this paper, we propose a stochastic process, which is a CoxIngersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. Laplace transforms and limit theorems have been obtained, including law of large numbe...

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi [1] for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case, Dereich, Neuenkirch and Szpruch [2] have shown recently a strong convergence of order 1/2 for this scheme. Here, we obtain a strong convergence of order 1 un...

Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility. The aim of this article is to present both, theoretical foundations and empirical aspects. Starting from the first short rate models, namely the Vasiček and the Cox-Ingersoll-Ross ones, we then give an overview of some properties of affi...

Ethical intuitionists like W.D. Ross adopt the common sense view that there is an irreducible plurality of types of ethically relevant considerations. They furthermore hold that there is no explicit method determining how to move from facts about which considerations are present to a conclusion about what it would be right to do. In order to systematize our moral reasoning, ethical intuitionist...

The famous Black-Sholes (BS) and Cox-Ross-Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a determinis...

This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that a drawdown of size a precedes a drawup of size b and vice versa. The results are applied to several ...

This paper asks whether neuroeconomics will make instrumental use of neuroscience to adjudicate existing disputes in economics or be more seriously informed by neuroscience in ways that might transform economics. The paper pursues the question by asking how neuroscience constructs an understanding of individuals as whole persons. The body of the paper is devoted to examining two approaches: Don...

In this work, we analyze two important and simple models of short rates, namely Vasicek and CIR models. The models are described and then the sensitivity of the models with respect to changes in the parameters are studied. Finally, we give the results for the estimation of the model parameters by using two different ways.

T he term structure models discussed in our previous article (“Term Structure of Interest Rates,” MiER Vol. 7, No. 3) such as the [Vasicek 1978] or the [CoxIngersoll-Ross 1985] model may not match the current term structure. The Black-Derman-Toy (BDT) and BlackKarasinksi models discussed in this article are important examples of models in which the current term structure can always be replicated.

Despite the considerable range of newly identified disease modifying approaches to the control of the inflammatory process reported over the past 10–20 years, only a few have yet gained widespread clinical acceptance. In contrast, the very recent advent of the class of anti-inflammatory agents termed COX-2 selective inhibitors is already having a significant impact on current clinical prescribi...