Title: Traditional and modern approaches to pricing in nonlife insurance Abstract: This thesis deals with the theory and implementation of generalized linear models in the area of pricing of non-life insurance and subsequent optimalization of rates. Using the generalized linear models it is possible to estimate expected value and variance of compound distribution of total claims made according to insurance policy during definite time period. The next step is to build an optimalization model and describe several methods how to determine rates that lead to optimal distribution of safety margins within insurance policies in particular risk groups. Represented approaches how to calculate insurance premiums are numerically illustrated on simulated data in concluding parts of the thesis.

In this thesis we are interested in generalized estimating equations (GEE). First, we introduce the term of generalized linear model, on which generalized estimating equations are based. Next we present the methos of pseudo maximum likelyhood and quasi-pseudo maximum likelyhood, from which we move on to the methods of generalized estimating equations. Finally, we perform simulation studies, which demonstrates the theoretical results presented in the thesis. 1

This bachelor’s thesis is a combined study of applied mathematical statistics and industrial engineering and management implemented to develop an algorithm which creates product combinations based on customer data analysis for eleven AB. Mathematically, generalized linear modelling, combinatorics and conditional probabilities were applied to create sales prediction models, generate potential combinations and calculate the conditional probabilities of the combinations getting purchased. SWOT analysis was used to identify which factors can enhance the sales from an industrial engineering and management perspective. Based on the regression analysis, the study showed that the considered variables, which were sales prices, brands, ratings, purchase countries, purchase months and how new the products are, affected the sales amounts of the products. The algorithm takes a barcode of a product as an input and checks whether if the corresponding product type satisfies the requirements of predicted sales amount and conditional probability. The algorithm then returns a list of possible product combinations that fulfil the recommendations. / Detta kandidatexamensarbete är en kombinerad studie av tillämpad matematisk statistik och industriell ekonomisk implementering för att utveckla en algoritm som skapar produktkombinationer baserad på kunddata analys för eleven AB. I den matematiska delen tillämpades generaliserade linjära modeller, kombinatorik och betingade sannolikheter för att skapa prediktionsmodeller för försäljningsantal, generera potentiella kombinationer och beräkna betingade sannolikheter att kombinationerna bli köpta. SWOT-analys användes för att identifiera vilka faktorer som kan öka försäljningen från ett industriell ekonomiskt perspektiv. Baserat på regressionsanalysen, studien har visat att de betraktade variablerna, som var försäljningspriser, varumärken, försäljningsländer, försäljningsmånader och hur nya produkterna är, påverkade försäljningsantalen på produkterna. Algoritmen tar emot en streckkod av en produkt som inmatning och kontrollerar om den motsvarande produkttypen uppfyller kraven för predikterad försäljningssumma och betingad sannolikhet. Algoritmen returnerar en lista av alla möjliga kombinationer på produkter som uppfyller rekommendationerna.

This bachelor thesis within mathematical statistics studies the possibility of modelling the renewal probability for commercial non-life insurance policyholders. The project was carried out in collaboration with the non-life insurance company If P&C Insurance Ltd. at their headquarters in Stockholm, Sweden. The paper includes an introduction to underlying concepts within insurance and mathematics and a detailed review of the analytical process followed by a discussion and conclusions. The first stages of the project were the initial collection and processing of explanatory insurance data and the development of a logistic regression model for policy renewal. An initial model was built and modern methods of mathematics and statistics were applied in order obtain a final model consisting of 9 significant characteristics. The regression model had a predictive power of 61%. This suggests that it to a certain degree is possible to predict the renewal probability of non-life insurance policyholders based on their characteristics. The results from the final model were ultimately translated into a measure of price sensitivity which can be implemented in both pricing models and CRM systems. We believe that price sensitivity analysis, if done correctly, is a natural step in improving the current pricing models in the insurance industry and this project provides a foundation for further research in this area. / Detta kandidatexamensarbete inom matematisk statistik undersöker möjligheten att modellera förnyelsegraden för kommersiella skadeförsärkringskunder. Arbetet utfördes i samarbete med If Skadeförsäkring vid huvudkontoret i Stockholm, Sverige. Uppsatsen innehåller en introduktion till underliggande koncept inom försäkring och matematik samt en utförlig översikt över projektets analytiska process, följt av en diskussion och slutsatser. De huvudsakliga delarna av projektet var insamling och bearbetning av förklarande försäkringsdata samt utvecklandet och tolkningen av en logistisk regressionsmodell för förnyelsegrad. En första modell byggdes och moderna metoder inom matematik och statistik utfördes för att erhålla en slutgiltig regressionsmodell uppbyggd av 9  signifikanta kundkaraktäristika. Regressionsmodellen hade en förklaringsgrad av 61% vilket pekar på att det till en viss grad är möjligt att förklara förnyelsegraden hos försäkringskunder utifrån dessa karaktäristika. Resultaten från den slutgiltiga modellen översattes slutligen till ett priskänslighetsmått vilket möjliggjorde implementering i prissättningsmodeller samt CRM-system. Vi anser att priskänslighetsanalys, om korrekt genomfört, är ett naturligt steg i utvecklingen av dagens prissättningsmodeller inom försäkringsbranschen och detta projekt lägger en grund för fortsatta studier inom detta område.

<p dir="ltr">Employee staffing and scheduling are critical aspects of resource management in labor-intensive, customer-centric service organizations. This thesis investigates the optimal decision-making process for these critical tasks in the presence of non-stationary uncertainty, such as case-mix resident need, recommended staffing hours, and potential staffing turnover, a challenge prevalent in various domains, including healthcare and nursing home management.</p><p dir="ltr">The research begins predicting resident needs accurately. For this purpose, we present a novel Bayesian modeling approach to predict nursing home need-based resident census and staffing time. The resultant time series data of need-based resident census and staffing time are nonstationary with potential correlations between resource utilization groups. We thus propose Bayesian latent variable models with time-varying latent states to capture the dynamic patterns of resident service needs. We demonstrate the superiority of the proposed Bayesian prediction models by comparing their forecasting performance with several popular benchmark models, using historical assessment and aggregate staffing data from representative nursing homes.</p><p dir="ltr">The thesis further incorporates a rolling-horizon scheduling approach that integrates a periodically evolving Bayesian forecasting method into a series of stochastic look-ahead decision actions over multiple periods. To deal with the workforce scheduling with nonstationary demand uncertainty, we introduce a stochastic lookahead optimization framework that executes two-stage stochastic programming periodically along a rolling horizon to address the evolving non-stationary uncertainty. We obtain two-stage stochastic programming models to design effective work schedules, specifically assigning nurses to various shifts while balancing the staff workload and accommodating fluctuating resident needs.</p><p dir="ltr">We finally introduce the SNHSSO framework (stochastic nursing home staffing and scheduling optimizer), encompassing data modeling and addressing multi-period, multi-uncertainty, and multi-objective staffing and scheduling challenges. When the SNHSSO Optimizer is executed with the provided inputs, it generates recommended staffing decisions for longer planning horizons, as well as schedules and contingency plans for shorter planning horizons. These adapted decisions and adjusted parameters are archived for future reference, facilitating subsequent iterations of the process. SNHSSO optimizes caregiver assignments by taking into account probabilistic forecasts of service requirements, resident acuity, and staff turnover, all within two-stage stochastic mixed integer linear programs. Our approach leverages a scenario-based rolling horizon methodology to effectively solve the SNHSSO model.</p><p dir="ltr">The empirical foundation of this work is built on case studies conducted using Minimum Data Set (MDS) data spanning five years from 2014 to 2018 in Indiana nursing homes.</p>

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<p>Postpartum depression has become a major public health concern for women within a specific time period after delivery. Depression is possibly associated with some risk factors such as socioeconomic status, social support, maternal mental and physical health, and history of anxiety. TOMIS III, funded by the Canadian Institutes of Health Research, is a prospective cohort to study the associations between delivery method and health and health resource utilization.</p> <p>Clinically, we investigated the associations between mode of delivery and outcome of postnatal depression, maternal and infant health, and we implied the risk predictors for outcomes by statistical methodology of marginal model with generalized estimating equations (GEE). Statistically, a variety of regression models, namely, generalized linear mixed effect model (GLMM), hierarchical generalized linear model (HGLM) and Bayesian hierarchical model were applied for this analysis and results were compared with GEEs. Some imputation strategies, namely, mean imputation, last observation carrying forward (LOCF), hot-deck imputation and multiple imputation were employed for handling missing values in this study.</p> <p>Analysis results demonstrated that there was no statistically significant association between mode of delivery and postpartum depression [OR 0.99, 95% CI (0.73, 1.34)]. However, the development of postpartum depression was found to be associated with low income, low mental and physical health functioning, lack of social support, the low number of unmet learning needs in hospital, and English or French spoken at home. Results were consistent for all regression models but GEE provided the best fit and an excellent discriminative ability. GEE models were constructed on different datasets imputed by mean, LOCF, hot-deck and multiple imputation, and LOCF was recommended to handle the missing data in this longitudinal study.</p> <p>Analyses on the outcome of maternal health and infant health stated that method of delivery had a statistically significant influence on maternal health but no significant impact on infant health. Risks of maternal health problems were associated with cesarean delivery, good/fair/poor infant health, low maternal mental and physical health functioning, lack of care for maternal mental health, and good/fair/poor health before pregnancy. Risks of infant health problems were associated with good/fair/poor maternal health before pregnancy and after discharge, inadequate care or help for infant health, fair/poor community services after discharge, low maternal mental health functioning, non-English or non-French spoken at home, and mothers born outside of Canada.</p> / Master of Science (MSc)

Depression, intertwined with sleep deprivation and self-esteem, presents a significant challenge to mental health worldwide. The research shown in this paper employs advanced statistical methodologies to unravel the complex interactions among these factors. Through log-linear homogeneous association, multinomial logistic regression, and generalized linear models, the study scrutinizes large datasets to uncover nuanced patterns and relationships. By elucidating how depression, sleep disturbances, and self-esteem intersect, the research aims to deepen understanding of mental health phenomena. The study clarifies the relationship between these variables and explores reasons for prioritizing depression research. It evaluates how statistical models, such as log-linear, multinomial logistic regression, and generalized linear models, shed light on their intricate dynamics. Findings offer insights into risk and protective factors associated with these variables, guiding tailored interventions for individuals in psychological distress. Additionally, policymakers can utilize these insights to develop comprehensive strategies promoting mental health and well-being at a societal level.

Multiple studies have documented declines of forest breeding birds in the eastern United States, but the temporal and spatial scales of most studies limit inference regarding large scale bird-habitat trends. A potential solution to this challenge is integrating existing long-term datasets such as the U.S. Forest Service Forest Inventory and Analysis (FIA) program and U.S. Geological Survey Breeding Bird Survey (BBS) that span large geographic regions. The purposes of this study were to determine if FIA metrics can be related to BBS population indices at multiple spatial and temporal scales and to develop predictive models from these relationships that identify forest conditions favorable to forest songbirds. I accumulated annual route-level BBS data for 4 species guilds (canopy nesting, ground and shrub nesting, cavity nesting, early successional), each containing a minimum of five bird species, from 1966-2004. I developed 41 forest variables describing forest structure at the county level using FIA data from for the 2000 inventory cycle within 5 physiographic regions in 14 states (AL, GA, IL, IN, KY, MD, NC, NY, OH, PA, SC, TN, VA, and WV). I examine spatial relationships between the BBS and FIA data at 3 hierarchical scales: 1) individual BBS routes, 2) FIA units, and 3) and physiographic sections. At the BBS route scale, I buffered each BBS route with a 100m, 1km, and 10km buffer, intersected these buffers with the county boundaries, and developed a weighted average for each forest variable within each buffer, with the weight being a function of the percent of area each county had within a given buffer. I calculated 28 variables describing landscape structure from 1992 NLCD imagery using Fragstats within each buffer size. I developed predictive models relating spatial variations in bird occupancy and abundance to changes in forest and landscape structure using logistic regression and classification and regression trees (CART). Models were developed for each of the 3 buffer sizes, and I pooled the variables selected for the individual models and used them to develop multiscale models with the BBS route still serving as the sample unit. At the FIA unit and physiographic section scales I calculated average abundance/route for each bird species within each FIA unit and physiographic section and extrapolated the plot-level FIA variables to the FIA unit and physiographic section levels. Landscape variables were recalculated within each unit and section using NCLD imagery resampled to a 400 m pixel size. I used regression trees (FIA unit scale) and general linear models (GLM, physiographic section scale) to relate spatial variations in bird abundance to the forest and landscape variables. I examined temporal relationships between the BBS and FIA data between 1966 and 2000. I developed 13 forest variables from statistical summary reports for 4 FIA inventory cycles (1965, 1975, 1989, and 2000) within NY, PA, MD, and WV. I used linear interpolation to estimate annual values of each FIA variable between successive inventory cycles and GLMs to relate annual variations in bird abundance to the forest variables. At the BBS route scale, the CART models accounted for > 50% of the variation in bird presence-absence and abundance. The logistic regression models had sensitivity and specificity rates > 0.50. By incorporating the variables selected for the models developed within each buffer (100m, 1km, and 10km) around the BBS routes into a multiscale model, I was able to further improve the performance of many of the models and gain additional insight regarding the contribution of multiscale influences on bird-habitat relationships. The majority of the best CART models tended to be the multiscale models, and many of the multiscale logistic models had greater sensitivity and specificity than their single-scale counter parts. The relatively fine resolution and extensive coverage of the BBS, FIA, and NLCD datasets coupled with the overlapping multiscale approach of these analyses allowed me to incorporate levels of variation in both habitat and bird occurrence and abundance into my models that likely represented a more comprehensive range of ecological variability in the bird-habitat relationships relative to studies conducted at smaller scales and/or using data at coarser resolutions. At the FIA unit and physiographic section scales, the regression trees accounted for an average of 54.1% of the variability in bird abundance among FIA units, and the GLMs accounted for an average of 66.3% of the variability among physiographic sections. However, increasing the observational and analytical scale to the FIA unit and physiographic section decreased the measurement resolution of the bird abundance and landscape variables. This limits the applicability and interpretive strength of the models developed at these scales, but they may serve as indices to those habitat components exerting the greatest influences on bird abundance at these broader scales. The GLMs relating average annual bird abundance to annual estimates of forest variables developed using statistical report data from the 1965, 1975, 1989, and 2000 FIA inventories explained an average of 62.0% of the variability in annual bird abundance estimates. However, these relationships were a function of both the general habitat characteristics and the trends in bird abundance specific to the 4-state region (MD, NY, PA, and WV) used for these analyses and may not be applicable to other states or regions. The small suite of variables available from the FIA statistical reports and multicollinearity among all forest variables further limited the applicability of these models. As with those developed at the FIA unit and physiographic sections scales, these models may serve as general indices to the habitat components exerting the greatest influences on bird abundance trends through time at regional scales. These results demonstrate that forest variables developed from the FIA, in conjunction with landscape variables, can explain variations in occupancy and abundance estimated from BBS data for forest bird species with a variety of habitat requirements across spatial and temporal scales. / Ph. D.

Semiparametric modeling is a hybrid of the parametric and nonparametric modelings where some function forms are known and others are unknown. In this dissertation, we have made several contributions to semiparametric modeling based on the single index model related to the following three topics: the first is to propose a model for detecting change points simultaneously with estimating the unknown function; the second is to develop two models for spatially correlated data; and the third is to further develop two models for spatially-temporally correlated data. To address the first topic, we propose a unified approach in its ability to simultaneously estimate the nonlinear relationship and change points. We propose a single index change point model as our unified approach by adjusting for several other covariates. We nonparametrically estimate the unknown function using kernel smoothing and also provide a permutation based testing procedure to detect multiple change points. We show the asymptotic properties of the permutation testing based procedure. The advantage of our approach is demonstrated using the mortality data of Seoul, Korea from January, 2000 to December, 2007. On the second topic, we propose two semiparametric single index models for spatially correlated data. One additively separates the nonparametric function and spatially correlated random effects, while the other does not separate the nonparametric function and spatially correlated random effects. We estimate these two models using two algorithms based on Markov Chain Expectation Maximization algorithm. Our approaches are compared using simulations, suggesting that the semiparametric single index nonadditive model provides more accurate estimates of spatial correlation. The advantage of our approach is demonstrated using the mortality data of six cities, Korea from January, 2000 to December, 2007. The third topic involves proposing two semiparametric single index models for spatially and temporally correlated data. Our first model has the nonparametric function which can separate from spatially and temporally correlated random effects. We refer it to "semiparametric spatio-temporal separable single index model (SSTS-SIM)", while the second model does not separate the nonparametric function from spatially correlated random effects but separates the time random effects. We refer our second model to "semiparametric nonseparable single index model (SSTN-SIM)". Two algorithms based on Markov Chain Expectation Maximization algorithm are introduced to simultaneously estimate parameters, spatial effects, and times effects. The proposed models are then applied to the mortality data of six major cities in Korea. Our results suggest that SSTN-SIM is more flexible than SSTS-SIM because it can estimate various nonparametric functions while SSTS-SIM enforces the similar nonparametric curves. SSTN-SIM also provides better estimation and prediction. / Ph. D.