Matematisk institutt
http://hdl.handle.net/10852/5
Sat, 16 Feb 2019 02:12:11 GMT
20190216T02:12:11Z

Pricing Perpetual American Options with Linear Programming
http://hdl.handle.net/10852/65671
Pricing Perpetual American Options with Linear Programming
Bakke, Jan Aleksander Olsen
This master thesis will demonstrate how to price perpetual American options with linear programming. American options are used both for hedging and speculation, and being able to price derivatives, without creating arbitrage opportunities, are of importance. First we introduce a deterministic security market model and exploit the mathematical structure. Then European and American put and call options are presented. With dynamic programming we show how to price American options. Dynamic programming is based on an idea that an investor would act optimally at all trading dates and the objective is yielding the maximum profit, despite the risk of not knowing the true future value of the option. With this technique, we investigate perpetual American options on a ternary Markov chain model. Perpetual options are without an expiration date. Markov chain models are only dependent of the current state when determining the future value, thus simplifying the computations. The solution, based on dynamic programming, is the smallest payoff that is greater than the discounted expected value of the option at the next trading date. The value and the payoff must not be confused, as an investor may be willing to pay more than the payoff today, if the value of the option might rise in the future. The solution is obtained by formulating the problem as an optimization problem and then using linear programming theory.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65671
20180101T00:00:00Z

Metoder og metodiske utfordringer for matchede kohortstudier
http://hdl.handle.net/10852/65639
Metoder og metodiske utfordringer for matchede kohortstudier
Johansen, Lena Rogstad
Når man estimerer effekten av en bestemt behandling eller eksponering på utfall i kohortstudier, og observasjonsstudier generelt, gir ikke standard metoder korrekte resultater i nærvær av ukontrollert konfundering. Matching er en teknikk som korrigerer for dette. I denne oppgaven studerer vi først og fremst i hvilken grad det er mulig å analysere matchede (også kalt tilordnede) kohortstudier når man ignorerer matchingsvariablene (konfunderingsvariablene) under forskjellige modellforutsetninger. Vi ser også på hvor mange ikkeeksponerte individer man bør velge per eksponert individ. Det viser seg at den estimerte sammenhengen mellom eksponering og utfall i nærvær versus fravær av matchingsvariablene avhenger av modellen for levetidene. Ettersom denne er både ukjent og ukontrollerbar i virkeligheten bør man beholde matchingsvariablene i analysen, såfremt det er mulig. Dessuten synes det å være lite å vinne på å velge flere enn ti ikkeeksponerte individer per eksponert individ.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65639
20180101T00:00:00Z

Bayesian model configuration, selection and averaging in complex regression contexts
http://hdl.handle.net/10852/65638
Bayesian model configuration, selection and averaging in complex regression contexts
Hubin, Aliaksandr
In this PhD thesis problems of Bayesian model selection and model averaging are addressed in various regression contexts. The approaches developed within the thesis are based on the idea of marginalizing out parameters from the likelihood. This allows to work on the marginal space of models, which simplifies the search algorithms significantly. For the linear models an efficient mode jumping Monte Carlo Markov chain (MJMCMC) algorithm was suggested. The approach performed very well on simulated and real data. Further, the algorithm was extended to work with logic regressions, where one has a feature space consisting of various complicated logical expressions, which makes enumeration of all features computationally and memory infeasible in most of the cases. The genetically modified MJMCMC (GMJMCMC) algorithm was suggested to tackle this issue. The algorithm combines the idea of keeping and updating the populations of highly predictive logical expressions combined with MJMCMC for the efficient exploration of the model space. Several simulation and real data studies show that logical expressions of high orders can be recovered with large power and low false discovery rate. Moreover, the GMJMCMC approach is adapted to make inference within the class of deep Bayesian regression models (which is a suggested in the thesis extension of various machine and statistical learning models like artificial neural networks, classification and regression trees, logic regressions and linear models). The reversible GMJMCMC, named RGMJMCMC, is also suggested. It makes transitions between the populations of variables in a way that satisfies the detailed balance equation. Based on several examples, it is shown that the DBRM approach can be efficient for both inference and prediction in various applications. In particular, two ground physical laws (planetary mass law and third Kepler’s law) were recovered from the data with large power and low false discovery rate. Three classification examples were also studied, where the comparison to other popular machine and statistical learning approaches was performed. Finally, a thorough study comparing different Bayesian approaches to genome wide association was done. It was shown that the developed in this thesis approaches can be efficiently applied to data with a huge number of covariates.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65638
20180101T00:00:00Z

Optimal control of forward–backward meanfield stochastic delayed systems
http://hdl.handle.net/10852/64791
Optimal control of forward–backward meanfield stochastic delayed systems
Agram, Nacira; Engen Røse, Elin
We study methods for solving stochastic control problems of systems offorward–backward meanfield equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The results are applied to solve a meanfield recursive utility optimal problem.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64791
20170101T00:00:00Z

Probabilistic boundaries of finite extensions of quantum groups
http://hdl.handle.net/10852/64601
Probabilistic boundaries of finite extensions of quantum groups
Malacarne, Sara; Neshveyev, Sergey
Given a discrete quantum group H with a finite normal quantum subgroup G, we show that any positive, possibly unbounded, harmonic function on H with respect to an irreducible invariant random walk is Ginvariant. This implies that, under suitable assumptions, the Poisson and Martin boundaries of H coincide with those of H/G. A similar result is also proved in the setting of exact sequences of C∗tensor categories. As an immediate application, we conclude that the boundaries of the duals of the grouptheoretical easy quantum groups are classical.
© 2017 World Scientific Publishing Company
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/64601
20170101T00:00:00Z

Simplex Splines on the PowellSabin 12Split
http://hdl.handle.net/10852/64070
Simplex Splines on the PowellSabin 12Split
Stangeby, Ivar Haugaløkken
In this thesis we implement and employ a simplex spline basis developed by Cohen, Lyche, and Riesenfeld for the space of C1 quadratic splines on the Powell–Sabin 12split of a triangle. A matrix recursion is used for evaluation and differentiation, where the need for standard Bernstein– Bézier techniques are avoided. A brief account of the construction of multivariate splines and the theoretical foundation underlying the finite element method is given. Subsequently, using an explicit conversion to the Hermite nodal basis known from the finite element method, we solve the biharmonic equation using conforming methods. Interpolation estimates are derived, and numerical results are seen to comply.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64070
20180101T00:00:00Z

Woronowicz TannakaKrein duality and free orthogonal quantum groups
http://hdl.handle.net/10852/63706
Woronowicz TannakaKrein duality and free orthogonal quantum groups
Malacarne, Sara
Given a finitedimensional Hilbert space H and a collection of operators between its tensor powers satisfying certain properties, we give a short proof of the existence of a compact quantum group G with a fundamental representation U on H such that the intertwiners between the tensor powers of U coincide with the given collection of operators. We then explain how the general version of Woronowicz TannakaKrein duality can be deduced from this.
© 2017 Mathematica Scandinavica
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/63706
20180101T00:00:00Z

Projected changes in significant wave height toward the end of the 21st century: Northeast Atlantic
http://hdl.handle.net/10852/63700
Projected changes in significant wave height toward the end of the 21st century: Northeast Atlantic
Aarnes, Ole Johan; Reistad, Magnar; Breivik, Øyvind; BitnerGregersen, Elzbieta M.; Eide, Lars Ingolf; Gramstad, Odin; Magnusson, Anne Karin; Natvig, Bent; Vanem, Erik
Wind field ensembles from six CMIP5 models force wave model time slices of the northeast Atlantic over the last three decades of the 20th and the 21st centuries. The future wave climate is investigated by considering the RCP4.5 and RCP8.5 emission scenarios. The CMIP5 model selection is based on their ability to reconstruct the present (1971–2000) extratropical cyclone activity, but increased spatial resolution has also been emphasized. In total, the study comprises 35 wave model integrations, each about 30 years long, in total more than 1000 years. Here annual statistics of significant wave height are analyzed, including mean parameters and upper percentiles. There is general agreement among all models considered that the mean significant wave height is expected to decrease by the end of the 21st century. This signal is statistically significant also for higher percentiles, but less evident for annual maxima. The RCP8.5 scenario yields the strongest reduction in wave height. The exception to this is the north western part of the Norwegian Sea and the Barents Sea, where receding ice cover gives longer fetch and higher waves. The upper percentiles are reduced less than the mean wave height, suggesting that the future wave climate has higher variance than the historical period.
© 2017 American Geophysical Union
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/63700
20170101T00:00:00Z

Multivariate modeling and analysis of regional ocean freight rates
http://hdl.handle.net/10852/63697
Multivariate modeling and analysis of regional ocean freight rates
Ådland, Roar Os; Benth, Fred Espen; Koekebakker, Steen
In this paper, we propose a new multivariate model for the dynamics of regional ocean freight rates. We show that a cointegrated system of regional spot freight rates can be decomposed into a common nonstationary market factor and stationary regional deviations. The resulting integrated CAR process is new to the literature. By interpreting the common market factor as the global arithmetic average of the regional rates, both the market factor and the regional deviations are observable which simplifies the calibration of the model. Moreover, forward contracts on the market factor can be traded in the Forward Freight Agreement (FFA) market. We calibrate the model to historical spot rate processes and illustrate the term structures of volatility and correlation between the regional prices and the market factor. Our model is an important contribution towards improved modelling and hedging of regional price risk when derivative market liquidity is concentrated in a single global benchmark.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/63697
20170101T00:00:00Z

A multiple treatment comparison metaanalysis of monoamine oxidase type B inhibitors for Parkinson's disease
http://hdl.handle.net/10852/63690
A multiple treatment comparison metaanalysis of monoamine oxidase type B inhibitors for Parkinson's disease
Binde, Caroline Ditlev; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent; Klemp, Marianne
Aims
To the best of our knowledge, there are no systematic reviews or meta‐analyses that compare rasagiline, selegiline and safinamide. Therefore, we aimed to perform a drug class review comparing all available monoamine oxidase type B (MAO‐B) inhibitors in a multiple treatment comparison.
Methods
We performed a systematic literature search to identify randomized controlled trials assessing the efficacy of MAO‐B inhibitors in patients with Parkinson's disease. MAO‐B inhibitors were evaluated either as monotherapy or in combination with levodopa or dopamine agonists. Endpoints of interest were change in the Unified Parkinson's Disease Rating Scale (UPDRS) score and serious adverse events. We estimated the relative effect of each MAO‐B inhibitor versus the comparator drug by creating three networks of direct and indirect comparisons. For each of the networks, we considered a joint model.
Results
The systematic literature search and study selection process identified 27 publications eligible for our three network analyses. We found the relative effects of rasagiline, safinamide and selegiline treatment given alone and compared to placebo in a model without explanatory variables to be 1.560 (1.409, 1.734), 1.449 (0.873, 2.413) and 1.532 (1.337, 1.757) respectively. We also found all MAO‐B inhibitors to be efficient when given together with levodopa. When ranking the MAO‐B inhibitors given in combination with levodopa, selegiline was the most effective and rasagiline was the second best.
Conclusions
All of the included MAO‐B inhibitors were effective compared to placebo when given as monotherapy. Combination therapy with MAO‐B inhibitors and levodopa showed that all three MAO‐B inhibitors were effective compared to placebo, but selegiline was the most effective drug.
This is the peer reviewed version of the, which has been published in final form by Wiley. This article may be used for noncommercial purposes in accordance with Wiley Terms and Conditions for Use of SelfArchived Versions.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/63690
20180101T00:00:00Z

Calibrating regionally downscaled precipitation over Norway through quantilebased approaches
http://hdl.handle.net/10852/63579
Calibrating regionally downscaled precipitation over Norway through quantilebased approaches
Bolin, David; Frigessi, Arnoldo; Guttorp, Peter; Haug, Ola; Orskaug, Elisabeth; Scheel, Ida; Wallin, Jonas
Dynamical downscaling of earth system models is intended to produce highresolution climate information at regional to local scales. Current models, while adequate for describing temperature distributions at relatively small scales, struggle when it comes to describing precipitation distributions. In order to better match the distribution of observed precipitation over Norway, we consider approaches to statistical adjustment of the output from a regional climate model when forced with ERA40 reanalysis boundary conditions. As a second step, we try to correct downscalings of historical climate model runs using these transformations built from downscaled ERA40 data. Unless such calibrations are successful, it is difficult to argue that scenariobased downscaled climate projections are realistic and useful for decision makers. We study both full quantile calibrations and several different methods that correct individual quantiles separately using random field models. Results based on crossvalidation show that while a full quantile calibration is not very effective in this case, one can correct individual quantiles satisfactorily if the spatial structure in the data are accounted for. Interestingly, different methods are favoured depending on whether ERA40 data or historical climate model runs are adjusted.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/63579
20160101T00:00:00Z

CR extensions with a classical Several Complex Variables point of view
http://hdl.handle.net/10852/62486
CR extensions with a classical Several Complex Variables point of view
Sonne, August Peter Brådalen
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/62486
20180101T00:00:00Z

Risk aggregation in Solvency II through recursive lognormals
http://hdl.handle.net/10852/62371
Risk aggregation in Solvency II through recursive lognormals
Bølviken, Erik; Guillen, Montserrat
It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the lognormal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish–Fisher type. The method handles taildependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the lognormal approximation and to demonstrate the importance of including taildependence. Arguably a lognormal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62371
20170101T00:00:00Z

The Copula Information Criteria
http://hdl.handle.net/10852/62370
The Copula Information Criteria
Grønneberg, Steffen; Hjort, Nils Lid
We derive two types of Akaike information criterion (AIC)‐like model‐selection formulae for the semiparametric pseudo‐maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model‐selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross‐validation copula information criterion, which exists under weak conditions and is a first‐order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.
The final version of this research has been published in the Scandinavian Journal of Statistics. © 2014 Wiley
Wed, 01 Jan 2014 00:00:00 GMT
http://hdl.handle.net/10852/62370
20140101T00:00:00Z

Distinct DNA methylation profiles in bone and blood of osteoporotic and healthy postmenopausal women
http://hdl.handle.net/10852/62369
Distinct DNA methylation profiles in bone and blood of osteoporotic and healthy postmenopausal women
Reppe, Sjur; Lien, Tonje Gulbrandsen; Hsu, YiHsiang; Gautvik, Vigdis Teig; Olstad, Ole Kristoffer; Yu, Rona; Bakke, Hege Gilbø; Lyle, Robert; Kringen, Marianne K.; Glad, Ingrid Kristine; Gautvik, Kaare M
DNA methylation affects expression of associated genes and may contribute to the missing genetic effects from genomewide association studies of osteoporosis. To improve insight into the mechanisms of postmenopausal osteoporosis, we combined transcript profiling with DNA methylation analyses in bone. RNA and DNA were isolated from 84 bone biopsies of postmenopausal donors varying markedly in bone mineral density (BMD). In all, 2529 CpGs in the top 100 genes most significantly associated with BMD were analyzed. The methylation levels at 63 CpGs differed significantly between healthy and osteoporotic women at 10% false discovery rate (FDR). Five of these CpGs at 5% FDR could explain 14% of BMD variation. To test whether blood DNA methylation reflect the situation in bone (as shown for other tissues), an independent cohort was selected and BMD association was demonstrated in blood for 13 of the 63 CpGs. Four transcripts representing inhibitors of bone metabolism—MEPE, SOST, WIF1, and DKK1—showed correlation to a high number of methylated CpGs, at 5% FDR. Our results link DNA methylation to the genetic influence modifying the skeleton, and the data suggest a complex interaction between CpG methylation and gene regulation. This is the first study in the hitherto largest number of postmenopausal women to demonstrate a strong association among bone CpG methylation, transcript levels, and BMD/fracture. This new insight may have implications for evaluation of osteoporosis stage and susceptibility.
The final version of this research has been published in Epigenetics. © 2017 Taylor & Francis
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/62369
20170101T00:00:00Z

Model uncertainty first, not afterwards
http://hdl.handle.net/10852/62368
Model uncertainty first, not afterwards
Glad, Ingrid Kristine; Hjort, Nils Lid
Watson and Holmes propose ways of investigating robustness of statistical decisions by examining certain neighbourhoods around a posterior distribution. This may partly amount to ad hoc modelling of extra uncertainty. Instead of creating neighbourhoods around the posterior a posteriori, we argue that it might be more fruitful to model a layer of extra uncertainty first, in the model building process, and then allow the data to determine how big the resulting neighbourhoods ought to be. We develop and briefly illustrate a general strategy along such lines.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/62368
20160101T00:00:00Z

A Boussinesq type extension of the GeoClaw model  a study of wave breaking phenomena applying dispersive long wave models
http://hdl.handle.net/10852/61411
A Boussinesq type extension of the GeoClaw model  a study of wave breaking phenomena applying dispersive long wave models
Kim, Jihwan; Pedersen, Geir Kleivstul; Løvholt, Finn; LeVeque, Randall J.
The nonlinear shallow water model is widely used in the study of tsunami propagation, but an increasing number of studies are dedicated to the dispersion dynamics of tsunamis. If the wave dispersion becomes important, Boussinesqtype models are often used. In this work, a general purpose Boussinesq solver, BoussClaw, is introduced for modeling nonlinear dispersive tsunami propagation, taking into account inundation. The BoussClaw model is an extension of the GeoClaw tsunami model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equations from the literature, which are based on the depthaveraged velocity and include enhanced dispersion properties. On the other hand, in the selected formulation only some nonlinearity is retained in the dispersion term. In order to validate BoussClaw, numerical results are compared to analytic solutions, solutions obtained by preexisting models, and laboratory experiments. Even though the equations of BoussClaw are not fully nonlinear they perform far better than standard Boussinesq equations with only linear dispersion terms. Furthermore, the wave steepening and breaking are carefully scrutinized, and we demonstrate that the point of wave breaking may be wrongly identified in many of the commonly used Boussinesq models.
Kim, Jihwan, et al. "A Boussinesq type extension of the GeoClaw modela study of wave breaking phenomena applying dispersive long wave models." Coastal Engineering 122 (2017): 7586.
© 2017. This manuscript version is made available under the CCBYNCND 4.0 license.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61411
20170101T00:00:00Z

Video production  mathematics for beginner students
http://hdl.handle.net/10852/61409
Video production  mathematics for beginner students
Kleppe, Johannes; Borge, Inger Christin
Beginner student courses in mathematics in higher education have had high failure rates across the country. A national study [1] conducted by the Norwegian Association of Higher Education Institutions (UHR) in 2013 showed that students need help with the transition from upper secondary school to university or college.
As one of the initiatives following this study, UHR joined forces with Centre for Research, Innovation and Coordination of Mathematics Teaching (MatRIC) financing the production of mathematics videos that would help students with the transition from upper secondary school to university or college.
A group of six people from four higher education institutions, all with experience from teaching mathematics to upper secondary school students and/or first year university students, formed the video production group. So far the group has produced over 100 videos with a total running time of over 1000 minutes. These videos are freely available to everyone at the MatRIC TV web site [2] as a national resource.
The production group has made several decisions about the presentation of the mathematical material and the design of the videos along the way. In this contribution to the MNT conference we will discuss these choices and our experiences with producing these videos, and also their impact.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61409
20170101T00:00:00Z

Computational Analysis of a Drag reducing Cone Grid
http://hdl.handle.net/10852/61358
Computational Analysis of a Drag reducing Cone Grid
Utnes, Anders
CFD analysis of a cone grid applied to a flat plate, with mesh generation script.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61358
20170101T00:00:00Z

Nodal finite element de Rham complexes
http://hdl.handle.net/10852/61204
Nodal finite element de Rham complexes
Christiansen, Snorre H; Hu, Jun; Hu, Kaibo
We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees with extra smoothness. Some of these elements have nodal degrees of freedom and can be considered as generalisations of scalar Hermite and Lagrange elements. Using the nodal values, the number of global degrees of freedom is reduced compared with the classical Nédélec and Brezzi–Douglas–Marini finite elements, and the basis functions are more canonical and easier to construct. Our finite elements for H(div) with regularity r=2 coincide with the nonstandard elements given by Stenberg (Numer Math 115(1):131–139, 2010). We show how regularity decreases in the finite element complexes, so that they branch into known complexes. The standard de Rham complexes of Whitney forms and their higher order version can be regarded as the family with the lowest regularity. The construction of the new families is motivated by finite element systems.
This is a postpeerreview, precopyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s002110170939x
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61204
20170101T00:00:00Z