Matematisk institutt
http://hdl.handle.net/10852/5
Wed, 11 Dec 2019 02:26:27 GMT2019-12-11T02:26:27ZThe Heston stochastic volatility model in Hilbert space
http://hdl.handle.net/10852/71465
The Heston stochastic volatility model in Hilbert space
Benth, Fred Espen; Simonsen, Iben Cathrine
We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein–Uhlenbeck process with itself. The volatility process is then defined by a Cholesky decomposition of the variance process. We define a Hilbert-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional and covariance operator of this process. This process is then applied to the modeling of forward curves in energy and commodity markets. Finally, we compute the dynamics of the tensor Heston volatility model when the generator is bounded, and study its projection down to the real line for comparison with the classical Heston dynamics.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/714652018-01-01T00:00:00ZApproximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models
http://hdl.handle.net/10852/71457
Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models
Benth, Fred Espen; Krühner, Paul
In this paper, we show how to approximate Heath–Jarrow–Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite-dimensional state space. Moreover, we recover a closed-form representation of the forward price dynamics in the approximation models and derive the rate of convergence to the true dynamics uniformly over an interval of time to maturity under certain additional smoothness conditions. In the Markovian case, we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/714572018-01-01T00:00:00ZGlobal simulations of Minkowski spacetime including spacelike infinity
http://hdl.handle.net/10852/71432
Global simulations of Minkowski spacetime including spacelike infinity
Doulis, Georgios; Frauendiener, Jörg
In this work, we study linearized gravitational fields on the entire Minkowski spacetime includingspacelike infinity. The generalized conformal field equations linearized about a Minkowski background areutilized for this purpose. In principle, this conformal representation of Einstein’s equations can be used tocarry out global simulations of Minkowski spacetime. We thoroughly investigate this possibility.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10852/714322017-01-01T00:00:00ZGraph products and the absence of property (AR)
http://hdl.handle.net/10852/71407
Graph products and the absence of property (AR)
Stammeier, Nicolai
We discuss the internal structure of graph products of right LCM semigroups and prove that there is an abundance of examples without property (AR). Thereby we provide the first examples of right LCM semigroups lacking this seemingly common feature. The results are particularly sharp for right-angled Artin monoids.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/714072018-01-01T00:00:00ZTopological comparison theorems for Bredon motivic cohomology
http://hdl.handle.net/10852/71359
Topological comparison theorems for Bredon motivic cohomology
Østvær, Paul Arne; Heller, Jeremiah; Voineagu, Mircea
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/713592019-01-01T00:00:00ZSearch for Good Examples of Hall's Conjecture
http://hdl.handle.net/10852/71352
Search for Good Examples of Hall's Conjecture
Aanderaa, Stål; Kristiansen, Lars; Ruud, Hans-Kristian
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713522018-01-01T00:00:00ZOn General Sum Approximations of Irrational Numbers
http://hdl.handle.net/10852/71341
On General Sum Approximations of Irrational Numbers
Georgiev, Ivan; Kristiansen, Lars; Stephan, Frank
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713412018-01-01T00:00:00ZPartial monitoring of multistate systems
http://hdl.handle.net/10852/71340
Partial monitoring of multistate systems
Skutlaberg, Kristina; Huseby, Arne; Natvig, Bent
For large multicomponent systems it is typically too costly to monitor the entire system constantly. In the presentpaper we consider a case where a component is unobserved in a time interval [0, T]. The time T is a stochasticvariable with a distribution which depends on the structure of the system and the lifetime distribution of theother components. Diﬀerent systems will result in diﬀerent distributions of T. The main focus is on how theunobserved period of time a ﬀects what we learn about the unobserved component during this period. Weanalyse this by considering one single component in three diﬀerent cases. In the ﬁrst case we consider both T aswell as the state of the unobserved component at time T as given. In the second case we allow the state of theunobserved component at time T to be stochastic, while in the third case both T and the state are treated asstochastic variables. In all cases we study the problem using preposterior analysis. That is, we investigate howmuch information we can expect to get by the end of the time interval [0, T]. The methodology is also illustratedon a more complex example.; Partial monitoring of multistate systems
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713402018-01-01T00:00:00ZExtensions to the boundary of Riemann maps on varying domains in the complex plane
http://hdl.handle.net/10852/71334
Extensions to the boundary of Riemann maps on varying domains in the complex plane
Pel, Jan; Peters, Han; Wold, Erlend Fornæss
We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713342018-01-01T00:00:00ZCombinatorial Perron Parameters for Trees
http://hdl.handle.net/10852/71333
Combinatorial Perron Parameters for Trees
Andrade, Enide; Ciardo, Lorenzo; Dahl, Geir
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/713332019-01-01T00:00:00ZNew bounds for the signless Laplacian spread
http://hdl.handle.net/10852/71332
New bounds for the signless Laplacian spread
Andrade, Enide; Dahl, Geir; Leal, Laura; Robbiano, Maria
Let G be an undirected simple graph. The signless Laplacian spread of G is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new bounds, both lower and upper, for the signless Laplacian spread. Several of these bounds depend on invariant parameters of the graph. We also use a minmax principle to find several lower bounds for this spectral invariant.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/713322019-01-01T00:00:00ZMajorization for matrix classes
http://hdl.handle.net/10852/71330
Majorization for matrix classes
Dahl, Geir; Guterman, Alexander; Shteyner, Pavel
We introduce a new majorization order for classes (sets) of matrices which generalizes several existing notions of matrix majorization. Roughly, the notion says that every matrix in one class is majorized by some matrix in the other class. The motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments. This connection is briefly described. We investigate properties of this new order both of algebraic and geometric character. In particular, we establish results on so-called minimal cover classes with respect to the introduced majorization.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713302018-01-01T00:00:00ZClimate change and safe design of ship structures
http://hdl.handle.net/10852/71328
Climate change and safe design of ship structures
Bitner-Gregersen, Elzbieta M.; Vanem, Erik; Gramstad, Odin; Hørte, Torfinn; Aarnes, Ole Johan; Reistad, Magnar; Breivik, Øyvind; Magnusson, Anne Karin; Natvig, Bent
The paper addresses projected changes of wave climate in the North Atlantic and their impact on the safe design of ships, with a particular focus given on associated uncertainties. The Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) uses four scenarios for future greenhouse gas concentrations in the atmosphere called Representative Concentration Pathways (RCP). Two of these scenarios are applied to investigate how sensitive the future North Atlantic wave climate is to the emissions they represent. Winds obtained from six global climate models have been used to simulate waves for a historical period at the end of last century and to project waves for a future period towards the end of this century for these two scenarios. Based on these projections, possible changes in extreme wind and waves are investigated and the associated uncertainties are discussed. The occurrence of rogue-prone sea states which may trigger generation of rogue waves in the past and future climate is also studied. It is shown how the scientific findings on uncertainties related to climate change projections and rogue waves can be incorporated in the risk-based approach used in current design practice of tankers, and ship structures in general. The potential effect of climate change on the safety level of current design practice for tankers is demonstrated. Finally, the paper discusses how structural design of ships can be upgraded to account for climate change and rogue waves without necessarily leading to significant economic consequences.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713282018-01-01T00:00:00ZTransit time and clogging of drops in constrictions
http://hdl.handle.net/10852/71325
Transit time and clogging of drops in constrictions
Fauli, Richard Andre
In this thesis, results from numerical simulations and experiments on drops squeezing through constricted capillaries are presented. The purpose is to understand how the capillary number changes how drops are deformed as they pass through constrictions and how long it takes them to do so. The simulations use the Cahn–Hilliard phase-field model and the Stokes equations to simulate both simple and compound drops, which are solved using the finite element method with FEniCS. The numerical implementation is validated using test cases such as the spreading of a viscous drop and the Laplace pressure jump in a drop. For the experiments, simple drops were generated using microfluidics techniques and PDMS- chip manufacturing. Experiments with about 300 drops at low Reynolds numbers are presented. The numerical and experimental results do not initially show good agreement, but when changing the viscosity of the two liquids in the simulations the results become more similar. We discuss some possible reasons why the results are different, including the possibility that the boundary conditions on the drop could have been changed because of the use of surfactants. The transit time for simple and compound drops are found for a range of capillary numbers and numerical results show that as the capillary number is reduced, the way the drops are squeezed through the constriction changes and for sufficiently low capillary numbers both simple and compound drops clog the capillary.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/713252019-01-01T00:00:00ZExposing boundary points of strongly pseudoconvex subvarieties in complex spaces
http://hdl.handle.net/10852/71324
Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
Deng, Fusheng; Fornæss, John Erik; Wold, Erlend Fornæss
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713242018-01-01T00:00:00ZPolar degrees and closest points in codimension two
http://hdl.handle.net/10852/71322
Polar degrees and closest points in codimension two
Helmer, Martin; Nødland, Bernt Ivar Utstøl
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713222018-01-01T00:00:00ZA convergent finite volume method for the Kuramoto equation and related non-local conservation laws
http://hdl.handle.net/10852/71318
A convergent finite volume method for the Kuramoto equation and related non-local conservation laws
Chatterjee, Neelabja; Fjordholm, Ulrik Skre
We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713182018-01-01T00:00:00ZComparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains
http://hdl.handle.net/10852/71316
Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains
Bracci, Filippo; Fornæss, John Erik; Wold, Erlend Fornæss
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713162018-01-01T00:00:00ZA non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary
http://hdl.handle.net/10852/71315
A non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary
Fornæss, John Erik; Wold, Erlend Fornæss
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713152018-01-01T00:00:00ZA single vibrionales 16S rRNA oligotype dominates the intestinal microbiome in two geographically separated Atlantic cod populations
http://hdl.handle.net/10852/71307
A single vibrionales 16S rRNA oligotype dominates the intestinal microbiome in two geographically separated Atlantic cod populations
Riiser, Even Sannes; Haverkamp, Thomas Hendricus Augustus; Borgan, Ørnulf; Jakobsen, Kjetill Sigurd; Jentoft, Sissel; Star, Bastiaan
Atlantic cod (Gadus morhua) provides an interesting species for the study of host-microbe interactions because it lacks the MHC II complex that is involved in the presentation of extracellular pathogens. Nonetheless, little is known about the diversity of its microbiome in natural populations. Here, we use high-throughput sequencing of the 16S rRNA V4 region, amplified with the primer design of the Earth Microbiome Project (EMP), to investigate the microbial composition in gut content and mucosa of 22 adult individuals from two coastal populations in Norway, located 470 km apart. We identify a core microbiome of 23 OTUs (97% sequence similarity) in all individuals that comprises 93% of the total number of reads. The most abundant orders are classified as Vibrionales, Fusobacteriales, Clostridiales, and Bacteroidales. While mucosal samples show significantly lower diversity than gut content samples, no differences in OTU community composition are observed between the two geographically separated populations. All specimens share a limited number of abundant OTUs. Moreover, the most abundant OTU consists of a single oligotype (order Vibrionales, genus Photobacterium) that represents nearly 50% of the reads in both locations. Our results suggest that these microbiomes comprise a limited number of species or that the EMP V4 primers do not yield sufficient resolution to confidently separate these communities. Our study contributes to a growing body of literature that shows limited spatial differentiation of the intestinal microbiomes in marine fish based on 16S rRNA sequencing, highlighting the need for multi-gene approaches to provide more insight into the diversity of these communities.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/713072018-01-01T00:00:00Z