Venture capitalists enter into an investment with the intent of realising a substantial profit on theventure after a number of years; this realisation is usually labelled the exit. The disinvestment decisionis a critical issue in the venture capital industry, as the return of the investment is realised upon exit.There are two important dimensions to the disinvestment decision; how and when to exit.This thesis studies the role of Venture Capital (VC) syndication, and its’ effect on exit dynamics for VCfirms in Sweden. The aspects of syndication will be focused on firm characteristics of investing parties,were the ambition is to provide an analysis of these characteristics and their effect on exit route(Merger and Acquisitions, M&As, and Initial Public Offerings, IPOs) and exit timing. Our statisticalanalysis rely on survival analysis with Competing Risk Models (CRM), which is adequate to model timein one state, when exit is to a number of competing states. These models allow for a joint analysis ofexit type and exit timing, i.e. model durations that end with multiple exits. Specifically, we apply theWeibull distribution with Gamma Frailty.To conduct the study, we have used a self-collected data set of 300 investments derived from 20 VCfirms in Sweden. For each investment, the data includes information relating to a number ofexplanatory variables concerning selected characteristics of the portfolio company and investingparties. Our results reveal that the presence of one or more experienced VC firms in the syndicatewould prolong time to exit and increase the likelihood of exiting through an IPO. We provided evidencethat a larger syndicate size will increase the time to exit and increase the likelihood for exiting throughan IPO. We also provided empirical evidence that foreign investor involvement in a syndicate prolongstime to exit in comparison to investments with only domestic co-investors and should affect exit routeby increasing the probability of an IPO. Finally, we could infer that a match between location of at leastone VC firm in a syndicate and acquirer country will have an increasing effect on time-to-exit, whileincreasing the probability of an exit in that country.We hope that the findings of this thesis will provide scholars and venture capitalists with novel,valuable information on a syndicates’ effect on exit dynamics.

In 2012, the U.S. Department of Health and Human Services reported an estimated 686,000 victims of child abuse and neglect. Forty-nine states reported a total of 1,593 fatalities. This quantitative research study examined the relationship between the variables: age of child, gender of child, age of parent/caregiver, prior substantiated reports of abuse, and incidents of abuse in Philadelphia at the Department of Human Services using risk practice model (RPM) and safety practice model (SPM). Although child welfare practitioners have examined the relationship between family and societal factors that affect child abuse; few researchers have examined the correlation between service delivery practice models and incidents of abuse. The findings of this quantitative study examined 34,761 components of variable data from the Department of Human Services revealed that the age of the child, age of the caregiver, and incidents of abuse are statistically significant predictors of abuse, whereas the gender of child had minimal effect on incidents of abuse. The most accurate predictor of child abuse is prior substantiated reports of abuse. The study shows that reports received in 2007 using the RPM were 9.6% more likely to have a valid report; likewise, every report received during the years 2007 and 2012 increases the probability of a valid report by 94.2%. Development of a comprehensive assessment tool that combines the principle tenets of both RPM and SPM is recommended. The implications for social change include developing a practice model that can increase safety probabilities while diminishing incidents of abuse by using a more comprehensive assessment tool.

Submitted by Vito Jarque Junior (vitojarque@gmail.com) on 2017-06-29T03:19:47Z No. of bitstreams: 1 Dissertação.pdf: 1824355 bytes, checksum: d2ac9c243606e99b445415fe2275c8fb (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2017-07-07T13:01:13Z (GMT) No. of bitstreams: 1 Dissertação.pdf: 1824355 bytes, checksum: d2ac9c243606e99b445415fe2275c8fb (MD5) / Made available in DSpace on 2017-07-21T14:49:19Z (GMT). No. of bitstreams: 1 Dissertação.pdf: 1824355 bytes, checksum: d2ac9c243606e99b445415fe2275c8fb (MD5) Previous issue date: 2017-05-30 / This work aims to quantify the credit risk of Brazilian companies, by using tools whose refinement and precision is more and more required by financial institutions on credit loans. In this regard, It is analyzed the credit spread and default probabilities derived by the application of two risk models, whose authors are Robert C. Merton (1974), and John Hull, Izzy Nelken and Alan White (2004). In the end, It is also evaluated the model with the best adherence to Brazilian market. / Este trabalho tem como objetivo quantificar o risco de crédito de empresas do mercado brasileiro, lançando mão de ferramentas cujo aprimoramento e precisão são cada vez mais exigidos pelas instituições financeiras nas concessões de empréstimos. Para isso, analisam-se o spread de crédito e a probabilidade de default gerados a partir da aplicação de dois modelos de avaliação de risco, cujos autores são, respectivamente, Robert C. Merton (1974), e John Hull, Izzy Nelken e Alan White (2004). Por fim, comparam-se e analisam-se os resultados, avaliando aquele com melhor aderência ao mercado brasileiro.

In present thesis we study and describe a stochastic loss reserve model for individual insurers. Specifically, it is the model based on the three following features. Modelling of expected claims depends on unknown parameters which estimates need to be the most accurate. Aggregated occurred and paid losses for particular years are modelled by a collective risk model. The final reserve is estimated by Bayesian methodology that uses a prior information from a significant number of insurers. Part of the thesis is also an implementation of the program that calculates reserves by using our model and its testing on simulated data.

Den här studien belyser hur revisorer i Sverige har påverkats av den globala finanskrisen. Inledningsvis presenteras tidigare skandaler och kriser som en bakgrund för studien, med anledning att upplysa läsaren om vilka konsekvenser det har fått för revisionsarbetet. Historiskt sett har yrket upprepade gånger haft motgångar som resulterat i hårdare krav och nya arbetsprocesser för revisorerna, där man gång på gång tvingats upprätthålla sitt förtroende och professionella status för allmänheten. Ämnet finner vi intressant eftersom det är under krissituationer som yrket prövas på allvar. För den här studien har vi valt en kvantitativ ansats som har baserats på en enkätundersökning. Enkäten har skickats till alla auktoriserade och godkända revisorer i landet, den utgörs av ett antal väl utvalda frågor som berör arbetsprocessen med risk som tema. Den teoretiska referensramen kommer att behandla revisorernas arbetsprocess och utförligt beskriva relevanta riskverktyg, tillgångsposter och begrepp. Teorin kommer att jämföras mot det empiriska materialet och sedan presenteras i en analys för studien. I resultatet kan vi konstatera att finanskrisen har haft en tydlig påverkan på revisionsarbetet. Det intressanta för studien är att vi har fått en bredare helhetssyn över hur revisorerna påverkats. Statistiska variabler har skapat förutsättningar för olika grupperingar och bidragit med värdefull information som har presenterats i analysen. Konsekvensen av finanskrisen har varit både positiva och negativa. Den ökade risken tvingar revisorerna till ett mer djupgående riskanalyser, detta upplever vi som en positiv konsekvens av finanskrisen. Även granskningsarbetet har fått ett ökat fokus och tvingat revisorerna till ett mer noggrannare arbete. En negativ konsekvens är att kraven för dokumentationen har ökat vilket skapat betydligt mer arbete för revisorerna, något som vi anser kan komma att påverka effektiviteten för revisionsarbetet.

<p>У дисертацији су изучавани модели одржавања на бази ризика и њихов утицај на поузданост парних турбина. У првом реду тежиште дисертације чини теоријско изучавање метода и модела одржавања на бази ризи-ка који ће се примењивати на поузданост и ризик ра-да парних турбина. Извршено је њихово прилагођа-вање како би били примењиви, као и њихов утицај на поузданост рада парних турбина. У дисертацији су развијени нови модели и то: Модел одржавања на бази ризика и његов утицај на поузданост парних турбина у виду алгоритма. Овај алгоритам подржава развијени математички мо-дел пет могућих стања, као и континуално праћење одређених дијагностичких параметара. На основу ве-личине одступања измерених од нормалних вредно-сти дијагностичких параметара оцењује се стање (степен неисправности) парних турбина и на основу тога доноси дијагностичка одлука о даљим активно-стима одржавања (о наставку или заустављања рада парне турбине). Помоћу овог алгоритамског праћења одређују се ста-ња: добро, задовољава, незадовољава, недозвољено Развијени модел могуће отказе компонената детекту-је у почетној фази настанка, чиме су створени услови за предузимањем правовремених одговарајућих ак-тивности одржавања. Откривањем деградационих стања компонената пру-жа се могућност да се у дијагностици стања утврде и идентификују неисправности које се у зависности од степена деградације поправљају и отклањају у што краћем року.<br />Други модел који је развијен је математички мо-дел пет стања и његова имплементација на поу-зданост парних турбина. У инжењерској пракси често се јављају проблеми одређивања оптималних временских интервала провере и поправке критичних склопова и компонената парних турбина, који се не могу одржавати током функционисања. Учесталост провере компонената, као што су парне турбине, довело би до непотребних високих трошкова. Међу-тим уколико би временски интервал између актив-ности одржавања био превелики, постојала би опас-ност од отказа компоненти што може резултовати значајним економским последицама а и ризик по<br />радно особље. Уведени модел пет могућих стања, у којима се парне турбине могу налазити, и помоћу кога се могу дефинисати стања парних турбина: опе-ративно стање(О), деградирано стање (D), стање ди-јагностиковања (DI), стање одржавања (М), и стање отказа (F), представља надоградњу Марковљевог мо-дела четири стања, јер је уведено ново пето стање ди-јагностика стања (DI). Модел служи за предикцију, спречавање отказа и сметње у раду парних турбина јер су одређени и предвиђени оптимални тренутци одржавања на годишњим нивоима као и вероватноће стања у оперативном стању, деградираном стању, стању у дијагностици, стању у одржавању и стању у отказу за пет и четири могућа стања, за једну, две, три и четири године у експлоатацији парних турбина. Ово је све израчунато нумерички, затим приказано табеларно и графички на дијаграмима. На крају је од-ређен времeнски и годишњи интервал генералног ремонта посматраних парних турбина На крају дисертације доказана је главна хипотеза која гласи: могуће је формирати моделе одржавања на бази ризика у циљу повишења нивоа поузданости парних турбина у процесу експлоатације. У закључку као срж дисертације, примена развијених нових мо-дела одржавања на бази ризика и њихов утицај на поузданост парних турбина доводи до више наведе-них закључака: Смањују број отказа и повећавају ни-во поузданости парних турбина, скраћују време у застоју (прекида у раду) погна и повећавају ниво расположивости, спречавају веће отказе и хаварије, а тиме и велике материјалне трошкове (финансиjске губитке), спречавају додатна оштећења и угрожавање рада целокупног погона, спречавају опасности по радно особље и околину, смањују активности класич-них превентивних активности, смањују активности непланираних корективних активности, остварују оп-тималне планиране активности одржавања и смањују непланиране трошкове одржавања.</p> / <p>U disertaciji su izučavani modeli održavanja na bazi rizika i njihov uticaj na pouzdanost parnih turbina. U prvom redu težište disertacije čini teorijsko izučavanje metoda i modela održavanja na bazi rizi-ka koji će se primenjivati na pouzdanost i rizik ra-da parnih turbina. Izvršeno je njihovo prilagođa-vanje kako bi bili primenjivi, kao i njihov uticaj na pouzdanost rada parnih turbina. U disertaciji su razvijeni novi modeli i to: Model održavanja na bazi rizika i njegov uticaj na pouzdanost parnih turbina u vidu algoritma. Ovaj algoritam podržava razvijeni matematički mo-del pet mogućih stanja, kao i kontinualno praćenje određenih dijagnostičkih parametara. Na osnovu ve-ličine odstupanja izmerenih od normalnih vredno-sti dijagnostičkih parametara ocenjuje se stanje (stepen neispravnosti) parnih turbina i na osnovu toga donosi dijagnostička odluka o daljim aktivno-stima održavanja (o nastavku ili zaustavljanja rada parne turbine). Pomoću ovog algoritamskog praćenja određuju se sta-nja: dobro, zadovoljava, nezadovoljava, nedozvoljeno Razvijeni model moguće otkaze komponenata detektu-je u početnoj fazi nastanka, čime su stvoreni uslovi za preduzimanjem pravovremenih odgovarajućih ak-tivnosti održavanja. Otkrivanjem degradacionih stanja komponenata pru-ža se mogućnost da se u dijagnostici stanja utvrde i identifikuju neispravnosti koje se u zavisnosti od stepena degradacije popravljaju i otklanjaju u što kraćem roku.<br />Drugi model koji je razvijen je matematički mo-del pet stanja i njegova implementacija na pou-zdanost parnih turbina. U inženjerskoj praksi često se javljaju problemi određivanja optimalnih vremenskih intervala provere i popravke kritičnih sklopova i komponenata parnih turbina, koji se ne mogu održavati tokom funkcionisanja. Učestalost provere komponenata, kao što su parne turbine, dovelo bi do nepotrebnih visokih troškova. Među-tim ukoliko bi vremenski interval između aktiv-nosti održavanja bio preveliki, postojala bi opas-nost od otkaza komponenti što može rezultovati značajnim ekonomskim posledicama a i rizik po<br />radno osoblje. Uvedeni model pet mogućih stanja, u kojima se parne turbine mogu nalaziti, i pomoću koga se mogu definisati stanja parnih turbina: ope-rativno stanje(O), degradirano stanje (D), stanje di-jagnostikovanja (DI), stanje održavanja (M), i stanje otkaza (F), predstavlja nadogradnju Markovljevog mo-dela četiri stanja, jer je uvedeno novo peto stanje di-jagnostika stanja (DI). Model služi za predikciju, sprečavanje otkaza i smetnje u radu parnih turbina jer su određeni i predviđeni optimalni trenutci održavanja na godišnjim nivoima kao i verovatnoće stanja u operativnom stanju, degradiranom stanju, stanju u dijagnostici, stanju u održavanju i stanju u otkazu za pet i četiri moguća stanja, za jednu, dve, tri i četiri godine u eksploataciji parnih turbina. Ovo je sve izračunato numerički, zatim prikazano tabelarno i grafički na dijagramima. Na kraju je od-ređen vremenski i godišnji interval generalnog remonta posmatranih parnih turbina Na kraju disertacije dokazana je glavna hipoteza koja glasi: moguće je formirati modele održavanja na bazi rizika u cilju povišenja nivoa pouzdanosti parnih turbina u procesu eksploatacije. U zaključku kao srž disertacije, primena razvijenih novih mo-dela održavanja na bazi rizika i njihov uticaj na pouzdanost parnih turbina dovodi do više navede-nih zaključaka: Smanjuju broj otkaza i povećavaju ni-vo pouzdanosti parnih turbina, skraćuju vreme u zastoju (prekida u radu) pogna i povećavaju nivo raspoloživosti, sprečavaju veće otkaze i havarije, a time i velike materijalne troškove (finansijske gubitke), sprečavaju dodatna oštećenja i ugrožavanje rada celokupnog pogona, sprečavaju opasnosti po radno osoblje i okolinu, smanjuju aktivnosti klasič-nih preventivnih aktivnosti, smanjuju aktivnosti neplaniranih korektivnih aktivnosti, ostvaruju op-timalne planirane aktivnosti održavanja i smanjuju neplanirane troškove održavanja.</p> / <p>The models of maintenance of the basis of risk, as well as their influence on reliability of steam turbines, are treated in this dissertation. First and foremost, the focus of the dissertation is the theo-retical study of the methods and the models of maintenance on the basis of risk, which will be applied to reliability and the risk of work of the steam turbines. Their adaptation has been treated in order for theam to be implemented, as well as their influence on reliability of the work of steam turbi-nes. New models are developed in the dissertation, and they are as follows: Model of maintenance on the basis of risk, as well as its influence on the reliability of steam turbines in form of algorithm. This algorithm supports the developed mathe-matical model of the five possible states, as well as the con-tinuaous monitoring of certain diagnostic parameters. The state (the degree of malfunction) is determined on the basis of value of deviation of the measured parameters from the desired value of the diagnostic parameters. Based on this, a diagnostic decision about the further activities of main-tenance will be made (about the continuation or the halt of the operation of the steam turbine). With this algorithmic tracking, the states are determined in the following manner: good, satisfying, unsatisfying, unpermitted. The developed model detects possible failures of the com-ponents in the initial phase of creation which creates the conditons for taking the maintenance action in a timely manner. By discovering the degradation states of component , there is a possiblility in the domain of the diagnostics f states to determine and identify irregularities tah are , depending on the stage of degradation, fixed in the shortest time possible.<br />The second model that is developed is the mathematical model of five states and its implementation on stam tur-bines reliability. In the engineering practice, problems that often occur are related to determination of the optimum time intervals of checkups and repair of the critical circuits and steam turbine components which can`t be maintain-edwhilw thwe machine is operating. Frequent checkups of components such as steam turbines might lead to unneces-sary high expenses. However, if the time interval between&nbsp;maintenance would be too long, the danger of the compo-nents failingwould increase, and that might result in signifi-cant economic consequences, as well as put the operating personnel to risk. The introduced model of five possible sta-tes of steam turbines, using which we can define the states of the steam turbines are: the operating state (O), the degra-ded state (D), the diagnosis state (DI), the maintenance state (M) and the failure state (F), represents the upgrade of the Marcovian model of four states, because the new fifth state , the diagnosis state (DI) has been introduced. The purpose of this model is to predict and prevent failure and break down in the functioning of the steam turbines, because the optimal moments of yearly maintenance, as well as the probability of the states in operating state, in degrated state, indiagnosis state, in maintenance state and in failure state for five and four possible states, for one, two, three and four years in the exploatation of the steam trurbines, are determined and pre-dicted. All of this has been numerically calculated, and then shown in tabular view, as well as graphically on the dia-grams. In the end, the time intervaland the yearly interval of general repair of the observed turbines are determined. In the end of dissertation, the main hypothesis is proven, and it states: it is possible to form the maintenance models on the basis of risk in order to increase the level of reliability of steam turbines in the process of exploatation, shorten the time in halt (interruption of the operating state) of the machines and they increase the level of availability, the prevent major faulires and breakdowns thereby preventing major material expenses (financial loss), they prevent additional damage and endangering of the work of the factory, they prevent the danger for the operating personnel and the environment, they decrease the activities needed for the ordinary preventive activities, they decrease the activitiesof the unpalnned corrective activities, they achieve the optimal palnned activities of maintenance and decrease the unplanned expenses of maintenance.</p>

<p>With 7 000 new cases in Sweden each year, breast cancer represents 30 percent of all female malignancies and is therefore the most commonly diagnosed cancer among women. There are limitations as to what can be done to prevent the disease but with the use of mammography screening the chances of finding and treating the disease at an early stage are increasing. Unfortunately, mammography screening is associated with radiation, which is an established risk factor for developing breast cancer. However, the newest screening technologies come with a reduced dose which decreases the risk of developing breast cancer due to the radiation.</p><p> </p><p>The effects of this lower dose compared to that of traditional technologies have not yet been studied and the purpose of this paper is therefore to assess the cost-effectiveness of the use of this new technology, with a focus on the number of radiation-induced cancers. A cost-utility analysis was performed where three different mammography technologies (one analogue and two digital) were compared. The total costs and QALYs of breast cancer generated by the use of these three technologies were calculated with the use of a Markov decision-analytic model, where a cohort of hypothetical 40 year-old women was followed throughout life.</p><p> </p><p>The results of the analysis showed that with the new digital technology (the PC-DR), one in 14 100 screened women develops breast cancer due to radiation while with the traditional mammography systems (SFM and the CR) this number is one in 3 500 and 4 300 screened women, respectively. Consequently, the number of induced cancers is decreased with up to 75 percent with the use of the PC-DR. Assuming that only the radiation dose differs between the three units, the analysis resulted in an incremental effect of 0.000269 QALYs over a life-time for the PC-DR when compared to SFM(0.000210 QALYs compared to the CR). The PC-DR was also associated with a 33 SEK (26 SEK) lower cost. Thus, if the only difference can be found in radiation dose, the PC-DR is the dominating technology to use since it is both more effective and costs less. However, it is possible that the PC-DR is more expensive per screening occasion than the other technologies and if so, the PC-DR would no longer be less costly. The study found that the scope for the possibility of excessive pricing is very small and under these circumstances, the willingness to pay for a QALY has to be considered when deciding what technology to invest in.</p>

Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8.

With 7 000 new cases in Sweden each year, breast cancer represents 30 percent of all female malignancies and is therefore the most commonly diagnosed cancer among women. There are limitations as to what can be done to prevent the disease but with the use of mammography screening the chances of finding and treating the disease at an early stage are increasing. Unfortunately, mammography screening is associated with radiation, which is an established risk factor for developing breast cancer. However, the newest screening technologies come with a reduced dose which decreases the risk of developing breast cancer due to the radiation.   The effects of this lower dose compared to that of traditional technologies have not yet been studied and the purpose of this paper is therefore to assess the cost-effectiveness of the use of this new technology, with a focus on the number of radiation-induced cancers. A cost-utility analysis was performed where three different mammography technologies (one analogue and two digital) were compared. The total costs and QALYs of breast cancer generated by the use of these three technologies were calculated with the use of a Markov decision-analytic model, where a cohort of hypothetical 40 year-old women was followed throughout life.   The results of the analysis showed that with the new digital technology (the PC-DR), one in 14 100 screened women develops breast cancer due to radiation while with the traditional mammography systems (SFM and the CR) this number is one in 3 500 and 4 300 screened women, respectively. Consequently, the number of induced cancers is decreased with up to 75 percent with the use of the PC-DR. Assuming that only the radiation dose differs between the three units, the analysis resulted in an incremental effect of 0.000269 QALYs over a life-time for the PC-DR when compared to SFM(0.000210 QALYs compared to the CR). The PC-DR was also associated with a 33 SEK (26 SEK) lower cost. Thus, if the only difference can be found in radiation dose, the PC-DR is the dominating technology to use since it is both more effective and costs less. However, it is possible that the PC-DR is more expensive per screening occasion than the other technologies and if so, the PC-DR would no longer be less costly. The study found that the scope for the possibility of excessive pricing is very small and under these circumstances, the willingness to pay for a QALY has to be considered when deciding what technology to invest in.

Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8.