We study the differentiability of the CIR process with respect to its parameters. We give a stochastic representation for these derivatives in terms of the paths of V .

Research on modeling time series text corpora has typically focused on predicting what text will come next, but less well studied is predicting when the next text event will occur. In this paper we address the latter case, framed as modeling continuous inter-arrival times under a logGaussian Cox process, a form of inhomogeneous Poisson process which captures the varying rate at which the tweets...

• 類推研究における 2種類の関係性構造の抽出 (Reeves & Weisberg, 1994) − Automatic schema abstraction > 複数事例の記憶・再生の経験によって抽出 > 新規問題に対しては,特徴の適合度に基づき貯蔵された事例が活性化し,その表象によって抽 象的スキーマが形成される (Goldinger, 1998; Hintzman, 1986) − Comparison-based abstraction (Strategic schema abstraction) > 問題同士を顕在的に比較するときに行われる > 2つの問題に共通する関係構造に着目し,その関係性構造が元の問題とは別に保存される (Kotovsky & Gentner, 1996; Namy & Gentner, 2002; Ross, 1984, 1989; Ross & ...

We consider the intensity-based approach for the modeling of default times of one or more companies. In this approach the default times are defined as the jump times of a Cox process, which is a Poisson process conditional on the realization of its intensity. We assume that the intensity follows the Cox-Ingersoll-Ross model. This model allows one to calculate survival probabilities and prices o...

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...