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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

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. ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

Når vi estimerer effekten av behandling for HIV vil ikke standard metoder gi korrekte resultater når vi har intermediate time-dependent confounders. Marginal Structural Models er en metode som kan brukes og vil korrigere ...

This thesis is divided into 4 chapters. Chapter 1 gives a brief explanation of what the Greeks are and why they are of interest in applied financial mathematics. There is also a short summary of the first attempts at ...

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 ...

This thesis addresses whether variance swaps should be part of an insurer's hedge strategy, and the replicating portfolio of a variance swap is derived and analysed to see if it creates a payout similar to the variance ...

We study optimal investments in rolling-horizon bond portfolios. Combinations of a money-market account and 1 to 3 rolling-horizon bonds are considered. Forward interest rates are modelled using finite dimensional realizations ...

In this thesis we analyze the performances of six different track and field disciplines (100m, 200m, 110m hurdles, 400m, 800m and 10000m) using mainly extreme value statistics. Besides fitting the generalized Pareto ...

Sampling techniques such as case-cohort and nested case-control studies, allows us to analyze survival data under the relative risk model assumption, without having to collect data for the full cohort. This can reduce the ...

I denne oppgaven ser vi på systemer som består av n komponenter. Systemet blir utsatt for en ytre belastning, og skal fordele denne belastningen på komponentene. Denne oppgaven omhandler hvordan vi skal belaste de ulike ...

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 ...

Parameter estimation is an important area of research, and over the years numerous different estimators have been proposed. One of the most popular ones is the maximum likelihood estimator, and in this thesis we discuss a ...

Projections of disability is an essential tool for insurance companies to set aside reserves for payouts. There are two main ideas behind the models of how this can be done, where one is by using static models and the other ...

I denne oppgaven gjør vi en romlig analyse på lammevekter som vil ha en geografisk tilhørighet til områder på både beitelagskala og kommuneskala. Ved å anta en varianskomponentmodell der vi spesifiserer områdene til å være ...

Biologists have great interest in studying sylvatic plague to give a better understanding of the process, but also to prevent plague from being transmitted to humans. I have studied the processes of sylvatic plague through ...

We study how to optimize oil production with respect to revenue in a situation where the production rate is uncertain. The oil production in a given period is described in terms of a difference equation, where this equation ...

Characteristic age patterns in future wage growth and job shifts are not considered in today’s actuarial calculations of defined benefit pension plans.Via the archives of the pensionconsulting firm GablerWassum, models for ...

Potenslov-demping av akustiske bølger er observert i komplekse medier som biologisk vev og de sedimentære lag av jordens øvre skorpe. Å forstå bølgeutbredelse gjennom slike medier er avgjørende for anvendelser i medisinsk ...

This thesis' goal is to model power forward contracts in the electricity marked with use of L\'evy processes. First we obtain some theory regarding these jump processes, which will enable us to built exponential additive ...

Ulike materialer reflekterer og absorberer forskjellige bølgelengder i ulik grad. Variasjon i disse egenskapene over et bredt spekter av bølgelengder gir materialer en unik spektral signatur. Hyperspektrale kameraer måler ...

This thesis describes, analyzes and applies the Solvency II on life and pension insurance by using the standard formulas in the Quantitative Impact Study 5 (QIS5) to calculate the Solvency Capital Requirement (SCR). We ...

In the last hundred years there have been a steady decline in mortality. When we are going to project how mortality is going to be in the future, we need a model who takes this decline in consideration. We have traditionally ...

Merton's portfolio problem tells us that given a risky asset modelled by a geometric Brownian motion and a risk-free asset modelled by a deterministic differential equation, the optimal trading strategy for a risk-averse ...

Forsikringsselskaper har til enhver tid forpliktelser til sine kunder, og det er viktig at selskapene har en god solvensmargin. Selskapene må sørge for å ha tilstrekkelig med kapital for å oppfylle forpliktelsene. Denne ...

Abstract The purpose of the following thesis is to study the effects of applying a Value-at-Risk constraint on the classic portfolio optimization problem. The Value at Risk constraint is thoroughly studied and a useful ...

A newly developed deterministic numerical model for air pollution from road traffic is combined with stochastic models in order to predict hourly average concentrations of nitrogen oxides (NOx) with estimated uncertainty. ...

Sammenligner forventete og observerte antall oligonukleotider av ulike lengder i mobile genetiske elementer og kromosomalt DNA. 108 komplett sekvenserte bakterie genomer, samt 180 plasmider og 371 fager inngår i analysen. ...

This thesis is divided into two parts. The first part involves the new solvency directive for the insurance industry in the European Union, Solvency II, which will be implemented in 2012. The second part involves valuation ...

Nested case-control studies (NCC) reduce the cost of large cohort studies, but are statistically less efficient since all information is only available for cases and controls. In particular in a competing risk situation ...

The purpose of the master thesis is to look at the classical article «Backward Stochastic Differential Equations in Finance» by Karoui, Peng and Quenez. Here, theory about Backward Stochastic Differential Equations (BSDEs) ...

Abstract Credit contagion arises when a company is in economic distress or if it defaults. The default of a company will have implications for any firm that is economically connected to this given company. The effect of ...

The present text examines and applies methods for modeling recurrent event data, focusing on whether to use global time or recurrence time as the basic time scale. The purpose is to gain an insight into how easy/difficult ...

Abstract Stochastic optimization using the stochastic Bellman equation, and probabilities approximated by way of Monte-Carlo, is a fairly unexplored field -- especially when the probabilities are affected by the controls. ...