Modeling Financial System with Interbank Flows, Borrowing, and Investing

In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. Each private actor aims to maximize its expected terminal logarithmic utility. The central bank, in turn, aims to control the overall economy by means of an exponential utility function. We solve all stochastic optimal control problems explicitly. We are able to recreate occasions such as liquidity trap. We study distribution of the number of defaults (net worth of a private actor going below a certain threshold).Comment: 27 pages, 29 figures. Keywords: systemic risk, stochastic control, principal-agent problem, stationary distribution, stochastic stability, Lyapunov functio

Fractional Generalizations of the Compound Poisson Process

This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its distributional properties, generalized fractional differential equations, and martingale properties. Some results related to the governing differential equation about the special cases of jump distributions, including exponential, Mittag-Leffler, Bernst\'ein, discrete uniform, truncated geometric, and discrete logarithm. Some of processes in the literature such as the fractional Poisson process of order $k$, P\'olya-Aeppli process of order $k$, and fractional negative binomial process becomes the special case of the GFCPP. Classification based on arrivals by time-changing the compound Poisson process by the inverse tempered and the inverse of inverse Gaussian subordinators are studied. Finally, we present the simulation of the sample paths of the above-mentioned processes.Comment: 20 pages, 12 figure

Testing a Goodwin model with general capital accumulation rate

We perform econometric tests on a modified Goodwin model where the capital accumulation rate is constant but not necessarily equal to one as in the original model (Goodwin, 1967). In addition to this modification, we find that addressing the methodological and reporting issues in Harvie (2000) leads to remarkably better results, with near perfect agreement between the estimates of equilibrium employment rates and the corresponding empirical averages, as well as significantly improved estimates of equilibrium wage shares. Despite its simplicity and obvious limitations, the performance of the modified Goodwin model implied by our results show that it can be used as a starting point for more sophisticated models for endogenous growth cycles.Comment: 39 page

Regression Monte Carlo for Microgrid Management

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid.Comment: CEMRACS 2017 Summer project - proceedings

Percutaneous release of trigger finger and its functional outcome

Background: An overview of percutaneous release for trigger finger and its functional outcomes. Methods: The present prospective controlled analytical study was conducted after taking approval from center human ethical committee. A written and informed consent was obtained. There were 50 patients who reported to outpatient department (OPD) with symptoms suggestive of trigger thumb/ finger, were subjected to the study. Results: Most of the patients belonged to the age group of 41-50 years. Majority of patients were females (56%) and males were (44%). Most of the patients had the right 1st digit involved (32%), followed by left 1st and right 3rd digit (18% each). Before the release of affected digit, 56% were grade 3, 26% were grade 4 and only 18% were grade 1. Complete resolution immediately after the procedure was seen in 82% cases. Pre procedure, mean VAS of 8.4 reduced to mean VAS of 6.2 immediate post procedure. At 48 hours post procedure, mean VAS of 3.06 and mean VAS of 1.12 was seen at 1-month post procedure period. At 3 months post procedure, mean VAS of 0.42. 94% cases had no complications. Conclusions: Percutaneous release of trigger finger is a safe and effective procedure associated with favorable functional outcomes. It provides an alternative treatment option for patients who have failed conservative management or prefer a minimally invasive approach

Automating question generation from educational text

The use of question-based activities (QBAs) is wide-spread in education, traditionally forming an integral part of the learning and assessment process. In this paper, we design and evaluate an automated question generation tool for formative and summative assessment in schools. We present an expert survey of one hundred and four teachers, demonstrating the need for automated generation of QBAs, as a tool that can significantly reduce the workload of teachers and facilitate personalized learning experiences. Leveraging the recent advancements in generative AI, we then present a modular framework employing transformer based language models for automatic generation of multiple-choice questions (MCQs) from textual content. The presented solution, with distinct modules for question generation, correct answer prediction, and distractor formulation, enables us to evaluate different language models and generation techniques. Finally, we perform an extensive quantitative and qualitative evaluation, demonstrating trade-offs in the use of different techniques and models.Comment: Accepted to AI-2023 (Forty-third SGAI International Conference on Artificial Intelligence) as a long paper, link: http://www.bcs-sgai.org/ai202

Regression Monte Carlo for microgrid management

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel consumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid