Parameter estimation in stochastic differential equations

Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to resolve. Thus we express them in a simplified manner of approximation by discretization and additive models based on splines. This defines a trilevel problem consisting of an optimization and a representation problem (portfolio optimization), and a parameter estimation (Weber et al. Financial Regression and Organization. In: Special Issue on Optimization in Finance, DCDIS-B, 2010). Two types of parameters dependency, linear and nonlinear, are considered by constructing a penalized residual sum of squares and investigating the related Tikhonov regularization problem for the first one. In the nonlinear case Gauss–Newton’s method and Levenberg–Marquardt’s method are employed in determining the iteration steps. Both cases are treated using continuous optimization techniques by the elegant framework of conic quadratic programming. These convex problems are well-structured, hence, allowing the use of the efficient interior point methods. Furthermore, we present nonparametric and related methods, and introduce into research done at the moment in our research groups which ends with a conclusion

Iterative methods for tomography problems: implementation to a cross-well tomography problem

The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz's algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values

Parameter estimation of Stochastic Logistic Model : Levenberg-Marquardt Method

In this paper, we estimate the drift and diffusion parameters of the stochas- tic logisticmodels for the growth of Clostridium Acetobutylicum P262 using Levenberg- Marquardt optimization method of non linear least squares. The parameters are esti- mated for five different substrates. The solution of the deterministic models has been approximated using Fourth Order Runge-Kutta and for the solution of the stochastic differential equations, Milstein numerical scheme has been used. Small values of Mean Square Errors (MSE) of stochastic models indicate good fits. Therefore the use of stochastic models are shown to be appropriate in modelling cell growth of Clostridium Acetobutylicum P26

IMPROVING CNN FEATURES FOR FACIAL EXPRESSION RECOGNITION

Abstract Facial expression recognition is one of the challenging tasks in computervision. In this paper, we analyzed and improved the performances bothhandcrafted features and deep features extracted by Convolutional NeuralNetwork (CNN). Eigenfaces, HOG, Dense-SIFT were used as handcrafted features.Additionally, we developed features based on the distances between faciallandmarks and SIFT descriptors around the centroids of the facial landmarks,leading to a better performance than Dense-SIFT. We achieved 68.34 % accuracywith a CNN model trained from scratch. By combining CNN features withhandcrafted features, we achieved 69.54 % test accuracy.Key Word: Neural network, facial expression recognition, handcrafted feature

Editorial: making an impact with optimization

The 27th European Conference on Operational Research, EURO XXVII, took place between 12–15 July 2015 at the University of Strathclyde in Glasgow, UK. In addition to three inspiring plenary sessions delivered by Tyrrell Rockafellar, Alan Wilson and Grazia Speranza, the conference also held eight keynote and three tutorial sessions by highly distinguished scholars. With over 2300 accepted abstract in over 100 streams, the conference provided an excellent environment for exposure to new ideas and collaboration opportunities

A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items

In this study, we develop an inventory model for deteriorating items with stock dependent demand rate. Shortages are allowed to this model and when stock on hand is zero, then the retailer offers a price discount to customers who are willing to back-order their demands. Here, the supplier as well as the retailer adopt the trade credit policy for their customers in order to promote the market competition. The retailer can earn revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. Besides this, we consider variable holding cost due to increase the stock of deteriorating items. Thereafter, we present an easy analytical closed-form solution to find the optimal order quantity so that the total cost per unit time is minimized. The results are discussed with the help of numerical examples to validate the proposed model. A sensitivity analysis of the optimal solutions for the parameters is also provided in order to stabilize our model. The paper ends with a conclusion and an outlook to possible future studies.Publisher's Versio