The objective of this thesis is to give a description of the rough stochastic volatility modelling based on fractional Brownian motion with Hurst exponent H less than 1/2, as well as the corresponding pricing model. ...

Reinsurance is a risk management tool for insurance companies, as it allows for transferring some of the insurance risk to reinsurance companies. From the insurer's perspective, a reinsurance contract may lead to more ...

Longitudinal data arise when repeated measurements are taken on individuals over time. Commonly used models for such data are multivariate linear models, linear mixed effect models and generalised linear mixed models. This ...

Solvency II er et forsikringsdirektiv som kontrollerer all forsikringsdrift i EU/EØS. Direktivet innebærer kontrollering av kapitalreserven, SCR, for hver av forsikringsselskapets porteføljer. Dette for å sikre forbrukerens ...

Regression analysis is a commonly used approach to modelling the relationships between dependent and independent variables. When estimating the coefficients of a regression model, the least squares estimator is often used, ...

Denne oppgaven handler om beregning av risiko for forsikringsutbetalinger ved vindkatastrofer, og hvordan Solvency II gir en forenklet måte å beregne kapitalkrav som skal sikre selskapene fra insolvens med 99.5% sikkerhet. ...

Usikkerhet rundt menneskers fremtidige levealder resulterer i stor risiko for livsforsikringsselskap. Retningslinene for kalkulering av slik risiko er satt av EU-kommisjonen og heter Solvency II. Denne oppgaven vil presenteres ...

In this thesis, we consider models for survival data with a high-dimensional covariate space. Most models used for such datasets are based on the Cox regression model, of which a critical assumption is that the hazard ...

In this thesis we analyze spread functions in the cointegrated market, with dynamics based on different combinations of Brownian motions and Ornstein-Uhlenbeck processes, and their structural differences. Theoretical and ...

In 1930, Fisher presented his fiducial argument as a solution to the "fundamen- tally false and devoid of foundation" practice of using Bayes’ theorem with uniform priors to represent ignorance about a parameter. His ...

The lower bounds are used to determine availabilities of a system, and are used in many different companies. Such is for example a company that supplies water to a city. The company would most likely want to know how ...

We build a mathematical model for the risk involved when a person makes a binding fixed-price offer to buy or sell something that fluctuates in value. This situation often arises in financial markets, where such an offer ...

On the 1st of January 2016, the Solvency II Directive regulating the European insurance industry came into force. Along with a host of reporting requirements, quantitative algorithms for calculating key quantities are ...

Computations in general insurance are often based on models such as the collective risk model, which uses a compound distribution to describe the aggregated losses. A critical part of this model is the un- certainty of ...

The traditional, linear representation of the genetic information in populations cause a loss of data, as it can not fully represent sites where the sequences differ. Conversely, a graph may incorporate the variation, ...

This thesis is devoted to presenting and illustrating a novel estimation method offering a way to reduce confounding bias in time-to-event situations. In order to reduce this bias, without having to observe all of the ...

The objectives of this thesis have been to model the spot prices in the energy market, to look at the forward curve, and to derive the Greeks from the spread option. The two energy commodities that have been used are power ...

Rubin (1987)’s combination formula for variance estimation in multiple imputation (MI) requires a imputation method to be Bayesian-proper. However, many census bureau have heavily relied on non-Bayesian imputations. Bjørnstad ...

The estimation of inverse covariance matrices plays a major role in portfolio optimization, for the global minimum variance portfolio in mean-variance analysis it is the only parameter used to determine the asset allocation. ...

Environmental contours are used as a basis for e.g., ship designs. The traditional approach to environmental contours is based on the well-known Rosenblatt transformation. However, due to the effects of this transformation ...

This thesis aims at pricing Contract-for-Difference (CFD) in stock market, and Electricity Price Area Differential (EPAD) in the Nord Pool. For CFD, our model consists of Geometric Brownian Motion and Vasicek process. For ...

With all the technological progress we have witnessed during the last couple of decades, it comes as no surprise that modern fraudsters use highly complex methods to disguise their suspicious activities. Traditional ...

In general insurance, the expected duration of a customer relationship is of great interest since retaining an existing customer is much cheaper than acquiring a new one from an administrative point of view. The expected ...

Norway has been suffering from numerous natural disasters throughout its history. In order to be able to compensate losses caused by natural disasters such as storm, flood, earthquake, avalanche or other natural disasters, ...

The spread of salmon lice has long been and continues to be an increasing problem for the fish farming industry, causing economic and environmental problems. In this thesis, in cooperation with the Norwegian Veterinary ...

In this thesis, we first present an overview of monotone regression, both in the classical setting and in the high dimensional setting. High dimensional data means that the number of covariates, p, exceeds the number of ...

The purpose of this thesis is to study the hedging of financial derivatives, using the so-called local risk-minimizing strategy, which is a popular quadratic hedging strategy in incomplete markets. The local risk minimization ...

Reserving against future claims and settlements is vital for insurance companies, in the sense that it influences how they may price their products and the solvency of the insurance company. This thesis will present and ...

In this thesis we simulate a new model, formulated as a nonlinear filtering problem with a generalized Cox process, for the modeling of transition rates in life insurance. This allows for a time-continuous model which may ...

The main result of my mine in the master thesis is a new Bismut-Elworthy-Li-formula with respect to a pure jump Levy noise driven stochastic differential equation (SDE), with non-Lipschitz continuous coefficients. This ...

Lending money has been one of the basic activities of banks for centuries. However, credit evaluation and pricing of loans are still not well understood, since the assessment of the impact of credit risk on prices in bond ...

Denne avhandlingen handler om optimal reforsikring. Reforsikring eller reassuranse er en type forsikring som forsikrer et forsikringsselskap. Et forsikringsselskap vil beskytte seg mot fremtidige store krav ved å overføre ...

In classic mathematical finance, a trader's actions have no direct influence on the asset price. For small trades this is a reasonable assumption, but large trades fire back at the underlying price. We consider a transient ...

Due to regulation reasons, life insurance undertakings have long been struggling with interest rate variations. In the post-financial-crisis era, most life insurance firms in Western countries are facing two major challenges, ...

Cox's regression model is one of the most used methods in medical statistics, and the method also finds applications in other fields. The purpose of the model is to explore the relationship between the effect of covariates ...

This thesis is devoted to the simultaneous estimation of the means of p> 1 independent Poisson distributions. A novel loss function that penalizes bad estimates of each of the means and the sum of the means is introduced. ...

I denne oppgaven var det som mål å komme frem til enkle dynamiske formuleringer og opplegg for fremskrivninger under kohort-baserte modeller. De vanligste dødelighetsmodeller i bruk i forsikring idag er baser på ...

Most insurance companies deal with reinsurance. One of the problems they have to solve is: What reinsurance treaty is optimal for their company? Optimal reinsurance for large portfolios has, during the past decades, been ...

The frequency of demands are crucial when analysing a safety instrumented system (SIS). IEC 61508 distinguishes between low and high demand mode when calculating risk for such a system. In reality there are systems that ...

A handful of special methods and techniques are available for solving the problems in insurance industries. The techniques are different based on the situation and each of these techniques has their own theory and logic. ...

The purpose of this thesis is to study the pricing of mortality risk in life annuities, when using the so-called Wang s Transform which is popular in certain quarters of actuarial science. This is a distortion operator ...

Cox's regression model is one of the most applied methods in medical research. This method finds also applications in other fields such as econometrics, demography, insurance etc. This method is based on two crucial ...

Mortality rates are the ratio of death counts and estimates of the population exposed to risk of deaths in matched intervals of time and age. Mortality forecasting is the use of historical data of mortality to determine ...

Mammographic screening is a method for detecting breast cancer at an early stage of the disease progression, and is thus considered a secondary prevention. The Norwegian Breast Cancer Screening Program invites all women ...

The Aalen-Johansen estimator for calculation of transition probabilities in a multi-state model, builds on the assumption that the data are Markovian. For real data, the Markov property may not be fulfilled, and it is then ...

A basic problem in large collections of documents is to find similar items, for basic search, recommendation, or other purposes. Traditionally techniques for this have relied only on the text in the document, since analysing ...

The Institute of Marine Research collects data from different sources for the estimation of fish abundance. These data can be divided into two groups: 1) Data from research surveys. 2) Fishery based data. In this thesis, ...

In 2008 Acerbi and Scandolo (see [?]) introduced a formalism to calculate portfolio values under the influence of liquidity risk. The formalism was used on asset portfolios, and stated that in the presence of liquidity ...

Estimators with cube root asymptotics are typically the result of M-estimation with non-smooth objective functions. Aside from being inefficient, they are hard to calculate, have intractable limiting distributions, and are ...

One objective of this Master thesis is to give an overview and discussion of the most important stochastic models for the dynamics of the yield surface. Since interest rates are of stochastic nature, and e.g. insurance ...

Vi ser på ulike måter å beregne korrelasjon mellom to variable på. Fokus er i stor grad på ordinale og kvantitative data og beregning av korrelasjonsmålene Pearson s r, Kendall s t og Spearman s rang-korrelasjon. Det ...

The main scope of this thesis is to implement a structured numerical analysis to check the exactness and applicability of the famous Kirk formula (1995) and the newer Bjerksund-Stensland formula (2011) widely used by energy ...

This master thesis gives an extensive survey of fundamental concepts in stochastic analy- sis like Itô s stochastic calculus and Malliavin calculus. These tools form the framework to numerically study the solutions of the ...

Reserving outstanding claims is crucial for insurance industry, in the sense that it influences both the cash balance (via pricing) and the solvency of the company. The main objective of this thesis has been to present and ...

This thesis is written in cooperation with Safetec, a leading provider of services within risk and reliability. The attention is aimed towards the oil and gas industry with the primary goal of improving the selection ...

In this thesis, we have studied the preselection bias that can occur when the number of covariates in a high dimensional regression problem is reduced prior to a high dimensional regression analysis like the lasso. Datasets ...

Usually, model selection is based on the merits of the model as such. However, in regression settings where the measurement we wish to estimate or predict is dependent on gathering relevant covariates, there are types of ...

Lee-Carter type modeller, og to-trinns estimering, er standardmetoden i demografi og forsikring, men den kan virke ustabil og følsom når parametrene skal bestemmes fra historiske data. En enkelt pensjonskasse eller ...

There are lots of special techniques and distribution models used to solve different problems in the insurance industry today. Learning the theory behind all of them is time consuming and leaves little time to analyze ...

With the new regulations of Basel III and Solvency II there is a necessity to have tools that can measure different types of financial and insurance risk in a portfolio. Stochastic Duration is such a measure. This new type ...

The Icelandic population is scarce compared to the Norwegian, causing high variability in the observed mortalities. We apply two mortality models to data on the Norwegian population dating 60 years back, and the Icelandic ...

The topic of this thesis is portfolio optimization under model ambiguity, i.e. a situation when the probability distribution of the events in the sample space is not known. The financial market studied is driven by a ...

A problem with the classical firm value model of Merton (1974) arises from modeling the firm value in terms of a diffusion. The resulting term structure of the credit spreads slopes upwards from zero, even for financially ...

Many families of distributions have been proposed to describe insurance losses. The process of finding the one which results in the best fit is time consuming. This thesis tries to tackle the issue of avoiding such analyses, ...

A number of methods have been developed for checking the fit of Cox regression models for cohort data; cf. chapter 11 in Klein & Moeschberger (2003, Springer-verlag). However, the methodology for model checking is much ...

In a situation where the number of available covariates greatly exceeds the number of observations, the fitting of a regression model to explain the connection between the response and the explanatory variables can be a ...

Vi tar utgangspunkt i artikkelen "Education and adult cause specific mortality-examining the impact of family factors shared by 871 367 Norwegian siblings". I denne studien ble sammenhengen mellom utdannelse og dødelighet ...

In this thesis I analyze two datasets about cervix cancer supplied by the Norwegian Radium Hospital. The datasets are measured by two different methods, the cDNA microarray technology and the Illumina BeadArray technology, ...

The object of this thesis is to study the classical Heath-Jarrow-Morton(HJM) model for interest rates, and the corresponding London Interbank Offered Rate(LIBOR) model, when the noise is driven by an It\^o-L\'evy process ...

Silverman(1986) tells about a 'recent surge' of interest density estimation. One of the theories discussed in the book is the kernel estimate, presented in Rosenblatt(1956) and Parzen(1962). This project is about using ...

Beregninger innenfor skadeforsikring tar ofte utgangspunkt i modeller. Derfor er det interessant å analysere modellfeil, der virkningene av slike feil i stigende grad vil bli mer aktuelt i skadeforsikring. Slike analyser ...

The main objective of this thesis has been to develop an analysis of the dynamics of exchange rates under two models; one continuous and one allowing for jumps. First we will look at a stochastic differential equation with ...

I denne oppgaven studerer og sammenligner vi to modeller for konkurrerende dødsårsaker; Cox proporsjonale modell for de årsaksspesifikke hasardratene (Cox 1972) og proporsjonal subfordelingsmodell(Fine & Gray 1999). For ...

Mixed-frequency variables may encounter problems of non-guaranteed steady-state in time-variant state-space system during temporal disaggregation, forecasting or nowcasting. The instability of state-space system directly ...

We study regime-switching models for stocks and interest rates. We define these models modifications of the classical models created by Black & Scholes and Vasicek for stocks and interest rates, respectively. The problem ...

I denne oppgaven brukes Kullback-Leibler divergens og bootstrap-simuleringer til å studere feil i velkjente dødelighetsmodeller anvendt i livsforsikring. Feil deles inn i tre kategorier; estimering-, modell- og ...

In this thesis we derive the price of a spread option based on two zero-coupon bonds. The two bonds will represent di erent nancial markets, and the HJM framework is used as the model for the underlying forward rates. We ...

This thesis investigates numerical methods for pricing options and forward contracts in Continuous Autoregressive Moving Average (CARMA) models. Via the Feynman-Kac connection between Markovian processes and Partial ...

The objective of this thesis is to value spread options with payoff function on the form max(S_1(T)-hS_2(T)-K,0), where S_1(T) and S_2(T) are the spot prices of two energy commodities at maturity time T, h is the heatrate ...

Oppgaven sammenlikner to strategier for hvordan en kan optimere olje- og gassproduksjonen fra flere reservoarer som deler et prosesseringsanlegg. Oljeproduksjonen i hver periode beskrives ved en differenslikning som ...

In this thesis we develop Focus Information Criteria (FIC) for a number of situations concerning model selection among nonparametric and parametric models. We mainly handle the one-sample case of fully observed independent ...