Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.Comment: 42 page

ROBUST PARAMETER DESIGN IN COMPLEX ENGINEERING SYSTEMS:

Many industrial firms seek the systematic reduction of variability as a primary means for reducing production cost and material waste without sacrificing product quality or process efficiency. Despite notable advancements in quality-based estimation and optimization approaches aimed at achieving this goal, various gaps remain between current methodologies and observed in modern industrial environments. In many cases, models rely on assumptions that either limit their usefulness or diminish the reliability of the estimated results. This includes instances where models are generalized to a specific set of assumed process conditions, which constrains their applicability against a wider array of industrial problems. However, such generalizations often do not hold in practice. If the realities are ignored, the derived estimates can be misleading and, once applied to optimization schemes, can result in suboptimal solutions and dubious recommendations to decision makers. The goal of this research is to develop improved quality models that more fully explore innate process conditions, rely less on theoretical assumptions, and have extensions to an array of more realistic industrial environments. Several key areas are addressed in which further research can reinforce foundations, extend existing knowledge and applications, and narrow the gap between academia and industry. These include the integration of a more comprehensive approach to data analysis, the development of conditions-based approaches to tier-one and tier-two estimation, achieving cost robustness in the face of dynamic process variability, the development of new strategies for eliminating variability at the source, and the integration of trade-off analyses that balance the need for enhanced precision against associated costs. Pursuant to a detailed literature review, various quality models are proposed, and numerical examples are used to validate their use

Stochastic simulation framework for the Limit Order Book using liquidity motivated agents

In this paper we develop a new form of agent-based model for limit order books based on heterogeneous trading agents, whose motivations are liquidity driven. These agents are abstractions of real market participants, expressed in a stochastic model framework. We develop an efficient way to perform statistical calibration of the model parameters on Level 2 limit order book data from Chi-X, based on a combination of indirect inference and multi-objective optimisation. We then demonstrate how such an agent-based modelling framework can be of use in testing exchange regulations, as well as informing brokerage decisions and other trading based scenarios

An Evaluation of Standard, Alternative, and Robust Slope Test Strategies

The robustness and power of nine strategies for testing the differences between two groups’ regression slopes under nonnormality and residual variance heterogeneity are compared. The results showed that three most robust slope test strategies were the combination of the trimmed and Winsorized slopes with the James second order test, the combination of Theil-Sen with James, and Theil-Sen with percentile bootstrapping. The slope tests based on Theil-Sen slopes were more powerful than those based on trimmed and Winsorized slopes

Modeling and Optimization of Stochastic Process Parameters in Complex Engineering Systems

For quality engineering researchers and practitioners, a wide number of statistical tools and techniques are available for use in the manufacturing industry. The objective or goal in applying these tools has always been to improve or optimize a product or process in terms of efficiency, production cost, or product quality. While tremendous progress has been made in the design of quality optimization models, there remains a significant gap between existing research and the needs of the industrial community. Contemporary manufacturing processes are inherently more complex - they may involve multiple stages of production or require the assessment of multiple quality characteristics. New and emerging fields, such as nanoelectronics and molecular biometrics, demand increased degrees of precision and estimation, that which is not attainable with current tools and measures. And since most researchers will focus on a specific type of characteristic or a given set of conditions, there are many critical industrial processes for which models are not applicable. Thus, the objective of this research is to improve existing techniques by not only expanding their range of applicability, but also their ability to more realistically model a given process. Several quality models are proposed that seek greater precision in the estimation of the process parameters and the removal of assumptions that limit their breadth and scope. An extension is made to examine the effectiveness of these models in both non-standard conditions and in areas that have not been previously investigated. Upon the completion of an in-depth literature review, various quality models are proposed, and numerical examples are used to validate the use of these methodologies