Publication Library
Monte-Carlo Estimation of CoVaR
Description: CoVaR is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo simulation-based batching estimator of CoVaR and study its consistency and asymptotic normality. We show that the optimal rate of convergence of the batching estimator is n−1/3, where n is the sample size. We then develop an importance-sampling inspired estimator under the delta-gamma approximations to the portfolio losses, and we show that the rate of convergence of the estimator is n−1/2. Numerical experiments support our theoretical findings and show that both estimators work well.
Created At: 14 December 2024
Updated At: 14 December 2024
A Causal Roadmap for Generating High-Quality Real-World Evidence
Description: Increasing emphasis on the use of real-world evidence (RWE) to support clinical policy and regulatory decision-making has led to a proliferation of guidance, advice, and frameworks from regulatory agencies, academia, professional societies, and industry. A broad spectrum of studies use real-world data (RWD) to produce RWE, ranging from randomized controlled trials with outcomes assessed using RWD to fully observational studies. Yet many RWE study proposals lack sufficient detail to evaluate adequacy, and many analyses of RWD suffer from implausible assumptions, other methodological flaws, or inappropriate interpretations. The Causal Roadmap is an explicit, itemized, iterative process that guides investigators to pre-specify analytic study designs; it addresses a wide range of guidance within a single framework. By requiring transparent evaluation of causal assumptions and facilitating objective comparisons of design and analysis choices based on pre-specified criteria, the Roadmap can help investigators to evaluate the quality of evidence that a given study is likely to produce, specify a study to generate high-quality RWE, and communicate effectively with regulatory agencies and other stakeholders. This paper aims to disseminate and extend the Causal Roadmap framework for use by clinical and translational researchers, with companion papers demonstrating application of the Causal Roadmap for specific use cases.
Created At: 14 December 2024
Updated At: 14 December 2024
Fundamental Theorem of Asset Pricing
Description: Fundamental Theorem of Asset Pricing
Created At: 14 December 2024
Updated At: 14 December 2024
The Probabilistic Method
Description: The Probabilistic Method has recently been developed intensively and became one of the most powerful and widely used tools applied in Combinatorics. One of the major reasons for this rapid development is the important role of randomness in Theoretical ComputerScience, a field which isrecently the source ofmany intriguing combinatorial problems. The interplay between Discrete Mathematics and Computer Science suggests an algorithmic point of view in the study of the Probabilistic Method in Combinatorics and thisis theapproach we triedtoadopt inthisbook. The manuscript thusincludesa discussion of algorithmic techniques together with a study of the classical method as well as the moderntoolsapplied init. The first part ofthe bookcontains a description of the tools applied in probabilistic arguments, including the basic techniques that use expectation and variance, as well as the more recent applications of Martingales and Correlation Inequalities. The second part includes a study of various topics in which probabilistic techniques have been successful. This part contains chapters on discrepancy and random graphs, as well as on several areas in Theoretical Computer Science; Circuit Complexity , Computational Geometry, and Derandomization of randomized algorithms. Scattered between the chapters are gems described under the heading"The Probabilistic Lens". Theseareelegant proofs that are not necessarily related to the chapters after which they appear and can be usually read separately.
Created At: 14 December 2024
Updated At: 14 December 2024
Monte Carlo Statistical Methods
Description: Monte Carlo Statistical Methods
Created At: 14 December 2024
Updated At: 14 December 2024