Uniqueness of Viscosity Solutions for Optimal Multi-Modes Switching Problem with Risk of default

In this paper we study the optimal m-states switching problem in finite horizon as well as infinite horizon with risk of default. We allow the switching cost functionals and cost of default to be of polynomial growth and arbitrary. We show uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem with risk of default. This problem is connected with the valuation of a power plant in the energy market.Comment: 25 pages; Real options, Backward stochastic differential equations, Snell envelope, Stopping times, Switching, Viscosity solution of PDEs, Variational inequalities. arXiv admin note: text overlap with arXiv:0805.1306 and arXiv:0904.070

Viscosity Solutions for a System of PDEs and Optimal Switching

In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases where such organizations or state grants or financial assistance to power plants that promotes green energy in their production activity or what uses less polluting modes in their production. We show existence for optimal strategy via a verification theorem then we show existence and uniqueness of the value processes by using an approximation scheme. In the markovian framework we show that the value processes can be characterized in terms of deterministic continuous functions of the state of the process. Those latter functions are the unique viscosity solutions for a system of $m$ variational partial differential inequalities with inter-connected obstacles.Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1102.1256, arXiv:0805.1306, arXiv:0904.0707, arXiv:1202.1108, and arXiv:0707.2663 and arXiv:1104.2689 by other authors. IMA Journal of Mathematical Control and Information (2016

Stochastic Optimal Control and BSDEs with Logarithmic Growth

In this paper, we study the existence of an optimal strategy for the stochastic control of diffusion in general case and a saddle-point for zero-sum stochastic differential games. The problem is formulated as an extended BSDE with logarithmic growth in the $z$-variable and terminal value in some $L^p$ space. We also show the existence and uniqueness of solution of this BSDE.Comment: 20 page

A Systematic Review of Tracing Solutions in Software Product Lines

Software Product Lines are large-scale, multi-unit systems that enable massive, customized production. They consist of a base of reusable artifacts and points of variation that provide the system with flexibility, allowing generating customized products. However, maintaining a system with such complexity and flexibility could be error prone and time consuming. Indeed, any modification (addition, deletion or update) at the level of a product or an artifact would impact other elements. It would therefore be interesting to adopt an efficient and organized traceability solution to maintain the Software Product Line. Still, traceability is not systematically implemented. It is usually set up for specific constraints (e.g. certification requirements), but abandoned in other situations. In order to draw a picture of the actual conditions of traceability solutions in Software Product Lines context, we decided to address a literature review. This review as well as its findings is detailed in the present article.Comment: 22 pages, 9 figures, 7 table

Optimal Multi-Modes Switching Problem in Infinite Horizon

This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as an extended impulse control problem and solved by means of probabilistic tools such as the Snell envelop of processes and reflected backward stochastic differential equations. A viscosity solutions approach is employed to carry out a finne analysis on the associated system of m variational inequalities with inter-connected obstacles. We show that the vector of value functions of the optimal problem is the unique viscosity solution to the system. This problem is in relation with the valuation of firms in a financial market

THE ROLE OF PRE-SERVICE TEACHER TRAINING IN DEVELOPING EFL TEACHERS' CLASSROOM MANAGEMENT COMPETENCY FOR BETTER TEACHING PERFORMANCE

Teachers’ role in improving the quality of the educational system is unquestionable. However, in order for teachers to fully and effectively play their role and help achieve the required educational objectives they have to be well-trained before their induction and the literature provides much evidence of this (Bozkuş, 2021). Hence, teacher pre-service training is a crucial stage in the early development of a teacher. The current study makes use of a mixed-method approach, including a questionnaire, semi-structured interviews, and observations to investigate the role of pre-service teacher training in developing EFL novice teacher classroom management competency. The participants were 43 Moroccan EFL novice middle school and high school teachers. The results showed that participants found classroom management challenging mainly due to the short and insufficient period of training in general and practicum in specific as well as the prioritization of theory over practice during training. Consequently, those novice teachers found themselves in a state of confusion about how to deal with such challenges which had an impact on their performance in the classroom.   Article visualizations