Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily bounded variation with a L\'evy measure concentrated on $(-1,\infty)$. We prove strong consistency and asymptotic normality for all admissible parameter values except one, where we show only weak consistency and mixed normal (but non-normal) asymptotic behavior. It turns out that the volatility of the price process is a measurable function of the price process. We also present some numerical illustrations to confirm our results.Comment: 51 pages, 3 figure

Parameter Estimation for the Square-root Diffusions : Ergodic and Nonergodic Cases

22 pagesThis paper deals with the problem of parameter estimation in the Cox-Ingersoll-Ross (CIR) model $(X_t)_{t\geq 0}$. This model is frequently used in finance for example as a model for computing the zero-coupon bound price or as a dynamic of the volatility in the Heston model. When the diffusion parameter is known, the maximum likelihood estimator (MLE) of the drift parameters involves the quantities : $\int_{0}^{t}X_sds$ and $\int_{0}^{t}\frac{ds}{X_s}$. At first, we study the asymptotic behavior of these processes. This allows us to obtain various and original limit theorems on our estimators, with different rates and different types of limit distributions. Our results are obtained for both cases : ergodic and nonergodic diffusion. Numerical simulations were processed using an exact simulation algorithm

Detection of semantic errors in Arabic texts

AbstractDetecting semantic errors in a text is still a challenging area of investigation. A lot of research has been done on lexical and syntactic errors while fewer studies have tackled semantic errors, as they are more difficult to treat. Compared to other languages, Arabic appears to be a special challenge for this problem. Because words are graphically very similar to each other, the risk of getting semantic errors in Arabic texts is bigger. Moreover, there are special cases and unique complexities for this language. This paper deals with the detection of semantic errors in Arabic texts but the approach we have adopted can also be applied for texts in other languages. It combines four contextual methods (using statistics and linguistic information) in order to decide about the semantic validity of a word in a sentence. We chose to implement our approach on a distributed architecture, namely, a Multi Agent System (MAS). The implemented system achieved a precision rate of about 90% and a recall rate of about 83%

Central Limit Theorem for the Multilevel Monte Carlo Euler Method and Applications to Asian Options

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [8] and significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg Feller type for the multilevel Monte Carlo method associated to the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [15], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the limiting variance in the central limit theorem of the algorithm. We investigate the application of the Multilevel Monte Carlo method to the pricing of Asian options, by discretizing the integral of the payoff process using Riemann and trapezoidal schemes. In particular, we prove stable law convergence for the error of these second order schemes. This allows us to prove two additional central limit theorems providing us the optimal choice of the parameters with an explicit representation of the limiting variance. For this setting of second order schemes, we give new optimal parameters leading to the convergence of the central limit theorem. Complexity analysis of the Multilevel Monte Carlo algorithm were processed

Identification and partial characterization of antifungal and antibacterial activities of two Bacillus sp. strains isolated from salt soil in Tunisia

Two Bacillus sp. strains (B29 and B27) isolated from soil in the South of Tunisia were tested for their abilities to produce antimicrobial compounds. Both strains showed antimicrobial activity against Gram-positive and Gram-negative bacteria, yeasts and fungi. The produced compounds were extracted by using four different solvents. The hexane solvent allowed to obtain maximum of activity of the strain B29. The activity of the strain B27 was not elucidated by the four solvents used. Bio-autography results of B29 hexane extract revealed presence of different antibiotics and antifungal compounds with different Rf values of 0.3 and 0.76 for antifungal compounds and of 0.12, 0.14, 0.19 and 0.3 for antibacterial ones. Two active fractions were isolated from the culture broth of the strain B29 by semi-preparative high performance liquid chromatography (HPLC). The partial sequencing of the 16S rDNA gene was used to identify the two Bacillus strains. They may be assigned to new Bacillus specie