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Linear Modeling for Insurance Ratemaking/Reserving: Modeling Loss Development Factors for Catastrophe Claims

Description

Catastrophe events occur rather infrequently, but upon their occurrence, can lead to colossal losses for insurance companies. Due to their size and volatility, catastrophe losses are often treated separately from other insurance losses. In fact, many property and casualty insurance

Catastrophe events occur rather infrequently, but upon their occurrence, can lead to colossal losses for insurance companies. Due to their size and volatility, catastrophe losses are often treated separately from other insurance losses. In fact, many property and casualty insurance companies feature a department or team which focuses solely on modeling catastrophes. Setting reserves for catastrophe losses is difficult due to their unpredictable and often long-tailed nature. Determining loss development factors (LDFs) to estimate the ultimate loss amounts for catastrophe events is one method for setting reserves. In an attempt to aid Company XYZ set more accurate reserves, the research conducted focuses on estimating LDFs for catastrophes which have already occurred and have been settled. Furthermore, the research describes the process used to build a linear model in R to estimate LDFs for Company XYZ's closed catastrophe claims from 2001 \u2014 2016. This linear model was used to predict a catastrophe's LDFs based on the age in weeks of the catastrophe during the first year. Back testing was also performed, as was the comparison between the estimated ultimate losses and actual losses. Future research consideration was proposed.

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2018-05

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Stochastic parameterization of the proliferation-diffusion model of brain cancer in a Murine model

Description

Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or

Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.

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2016-05

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Estimating GL-261 cell growth: A murine model for Glioblastoma Multiforme

Description

Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter

Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.

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2014-05

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Quantifying the Mortality Impact of the 1918-1919 Influenza Pandemic in Arizona

Description

Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess

Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.

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2015-05

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Modeling Surface Brightness of the HH 901 Jets in the Carina Nebula

Description

The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission

The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission line data for [Fe II] 12660 Å, Hα 6563 Å, and [S II] 6720 Å to compare with Hubble Space Telescope observations of the HH 901 jets presented in Reiter et al. (2016). We derived the emissivities for these lines from the spectral synthesis code Cloudy by Ferland et al. (2017). In addition, we used WENO simulations of density, temperature, and radiative cooling to model the jet. We found that the computed surface brightness values agreed with most of the observational surface brightness values. Thus, the 3D cylindrically symmetric simulations of surface brightness using the WENO code and Cloudy spectral emission models are accurate for jets like HH 901. After detailing these agreements, we discuss the next steps for the project, like adding an external ambient wind and performing the simulations in full 3D.

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2020-05

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Homeward Bound: An Overview of Continuing Care at Home

Description

AARP estimates that 90% of seniors wish to remain in their homes during retirement. Seniors need assistance as they age, historically they have received assistance from either family members, nursing homes, or Continuing Care Retirement Communities. For seniors not wanting

AARP estimates that 90% of seniors wish to remain in their homes during retirement. Seniors need assistance as they age, historically they have received assistance from either family members, nursing homes, or Continuing Care Retirement Communities. For seniors not wanting any of these options, there has been very few alternatives. Now, the emergence of the continuing care at home program is providing hope for a different method of elder care moving forward. CCaH programs offer services such as: skilled nursing care, care coordination, emergency response systems, aid with personal and health care, and transportation. Such services allow seniors to continue to live in their own home with assistance as their health deteriorates over time. Currently, only 30 CCaH programs exist. With the growth of the elderly population in the coming years, this model seems poised for growth.

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2019-05

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Automating by Developing Model Components for the Insurance Ratemaking Actuarial Procedures

Description

The objective of this study is to build a model using R and RStudio that automates ratemaking procedures for Company XYZ’s actuaries in their commercial general liability pricing department. The purpose and importance of this objective is to allow actuaries

The objective of this study is to build a model using R and RStudio that automates ratemaking procedures for Company XYZ’s actuaries in their commercial general liability pricing department. The purpose and importance of this objective is to allow actuaries to work more efficiently and effectively by using this model that outputs the results they otherwise would have had to code and calculate on their own. Instead of spending time working towards these results, the actuaries can analyze the findings, strategize accordingly, and communicate with business partners. The model was built from R code that was later transformed to Shiny, a package within RStudio that allows for the build-up of interactive web applications. The final result is a Shiny app that first takes in multiple datasets from Company XYZ’s data warehouse and displays different views of the data in order for actuaries to make selections on development and trend methods. The app outputs the re-created ratemaking exhibits showing the resulting developed and trended loss and premium as well as the experience-based indicated rate level change based on prior selections. The ratemaking process and Shiny app functionality will be detailed in this report.

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Date Created
2022-05

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Game Theory and its Applications to Infrastructure Security: A Bibliometric Analysis

Description

Game theory, the mathematical study of mathematical models and simulations that often play out like a game, is applicable to a plethora of disciplines, one of which is infrastructure security. This is a rather new and niche subject area, and

Game theory, the mathematical study of mathematical models and simulations that often play out like a game, is applicable to a plethora of disciplines, one of which is infrastructure security. This is a rather new and niche subject area, and our aim is to perform a bibliographic analysis to analyze the thematic makeup of a selected body of publications in this area, as well as analyze trends in paper publication, journal contributions, country contributions, and trends in the authorship of the publications.

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2022-05

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Mathematical Assessment of the Impact of Insecticide-Based Intervention on Malaria Transmission Dynamics

Description

Malaria is a deadly, infectious, parasitic disease which is caused by Plasmodium parasites and transmitted between humans via the bite of adult female Anopheles mosquitoes. The primary insecticide-based interventions used to control malaria are indoor residual spraying (IRS) and long-lasting

Malaria is a deadly, infectious, parasitic disease which is caused by Plasmodium parasites and transmitted between humans via the bite of adult female Anopheles mosquitoes. The primary insecticide-based interventions used to control malaria are indoor residual spraying (IRS) and long-lasting insecticide nets (LLINs). Larvicides are another insecticide-based intervention which is less commonly used. In this study, a mathematical model for malaria transmission dynamics in an endemic region which incorporates the use of IRS, LLINS, and larvicides is presented. The model is rigorously analyzed to gain insight into the asymptotic stability of the disease-free equilibrium. Simulations of the model show that individual insecticide-based interventions will not realistically control malaria in regions with high endemicity, but an integrated vector management strategy involving the use of multiple interventions could lead to the effective control of the disease. This study suggests that the use of larvicides alongside IRS and LLINs in endemic regions may be more effective than using only IRS and LLINs.

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2022-05

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Looking at COVID-19 as a Factor in Insurance Loss Reserving Models

Description

A factor accounting for the COVID-19 pandemic was added to a generalized linear model to more accurately predict unpaid claims. COVID-19 has affected not just healthcare, but all sectors of the economy. Because of this, whether or not an automobile

A factor accounting for the COVID-19 pandemic was added to a generalized linear model to more accurately predict unpaid claims. COVID-19 has affected not just healthcare, but all sectors of the economy. Because of this, whether or not an automobile insurance claim is filed during the pandemic needs to be taken into account while estimating unpaid claims. Reserve-estimating functions such as glmReserve from the “ChainLadder” package in the statistical software R were experimented with to produce their own results. Because of their insufficiency, a manual approach to building the model turned out to be the most proficient method. Utilizing the GLM function, a model was built that emulated linear regression with a factor for COVID-19. The effects of such a model are analyzed based on effectiveness and interpretablility. A model such as this would prove useful for future calculations, especially as society is now returning to a “normal” state.

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2022-05