Hyressättningen i Sverige har de senaste decennierna utstått kritik för sin icke-konkreta struktur. Som svar, infördes år 2003 en ny modell för hyresprissättning av lägenheter i Malmö. Modellen fick namnet Malmömodellen och består av 180 parametrar som värderar lägenheter utifrån standard och läge. Parametervärden kombinerat med typ och yta av lägenhet definierar riktlinjen för vilken hyra fastighetsägare har rätt att debitera hyresgästen. Malmömodellen har givit en väldefinierad utgångspunkt för hyressättning men också tydliggjort var extra intäkter kan genereras genom investeringar i befintliga fastighetsbestånd - via så kallade standardhöjningar. Investeringarna värderas enligt Malmömodellen i proportion till lägenhetens storlek. Fastighetsbranschen, som kännetecknas av långsiktig förvaltning har i allmänhet inte insett modellens fulla värde. Kännedomen anses låg inom sektorn och bolagen använder förenklade prismodeller som är enklare att överse men som inte alltid är optimala för vinstmaximering. Standardhöjning kräver hyresgästens godkännande. Baserat på statistiskt data avseende tidigare erbjudande av standardhöjning har betalningsviljan i förhållande till typ och storlek på lägenhet undersökts och modellerats. Resultatet visar en högre betalningsvilja i större lägenheter vilket innebär förlorad avkastning vid en jämnt fördelad prisstrategi i fastighetsbestånd med stora lägenheter. Rapporten visar att det för varje fastighet finns en optimal prisstrategi för standardhöjning som är en kombination av Malmömodellens riktlinjer och den förenklade prismodellen. Priset bör bestå av en rörlig del proportionerlig mot den relativa hyran och en fast del. Den optimala prisstrategin beror på lägenhetsfördelning i fastigheten, betalningsvilja och investeringskostnad. Vidare kritiseras Malmömodellen för att dess transperens missgynnar nödvändiga investeringar med låg avkastning. Framförallt missgynnas socialt utsatta områden där betalningsviljan är låg. Diskussionen kretsar också kring för och nackdelar utifrån de nationalekonomiska effekter som ett reglerat pristak skapar. / Rental pricing in Sweden have endured criticism the latest decades due to its non-concrete structure. As an answer to this, in year 2003, Malmö introduced a new model for valuing rental prices for apartments. The model was named Malmömodellen and consists of 180 parameters valuing apartment standard and location. The parameter-value combined with type of apartment and size defines the guidelines for allowed pricing by landlords. The model has well defined the basis for rents but also highlighted were extra revenue can be generated through investments in existing holdings - by so called Standardhöjning. The Swedish real estate sector is characterized by longterm management and has not yet recognized the full potential in the model. Companies are applying simplified models, which are easier to overlook but not always optimal in terms of profit maximization. Investments in apartmens is conditioned by the tenants acceptence. Based on statistical data regarding earlier offering of standardhöjning, the willingness to pay in relationship to type and size of apartments has been analyzed and modelled. The result shows that the willingness to pay is higher in larger apartments which implies that revenue is being lost by applying a simplified model. The report shows that for every property there is an optimal pricing strategy which is a combination of the guidelines in Malmömodellen and a simplified model. The price should consist of a floating part proportional to the size of the apartment and a fixed part. The optimal pricing stragy depends on the distribution of apartments within the property and the investment cost. The model is further criticized due to its transparency disfavouring necessary investments with low returns. This especially penalize socially vurnable areas were the willingness to pay is low. The discussion takes into consideration the pros and cons regarding the economic effects of a regulated price cap.

This thesis empirically evaluates a geometric Brownian motion and a stochastic volatility model for modeling futures prices and hedging Asian call options on the electricity spot price. Estimation of parameters for the models is done based on historical futures prices of futures contracts with a one month delivery period using nonlinear regression and Maximum Likelihood techniques. The models are tested on 2014 data and tracking error for each model is presented. The tracking error is investigated through the median value, the spread between minimum and maximum value along with value at risk at a 95% level. In addition, a third model for modeling spot and futures prices is presented theoretically. It is an exponential additive model with the advantage that it models the future price process from the spot price, instead of modeling the future price process immediately. This bypasses the issue of no information about the future price process during the delivery period, when there is no prices of the futures contracts. The aim of this thesis is to compare the simpler geometric Brownian motion to the more complex stochastic volatility model. It is found that the stochastic volatility model performs better when tested on out-of-sample data. The geometric Brownian motion tends to underestimate the electricity prices, despite that 2014 had low pricest compared to the other years in the data sample. In addition, the approximation of the distribution of the future price process under the geometric Brownian motion model gave a bad fit and led to difficulties when estimating the parameters. The stochastic volatility model produced more stable results and gave a better fit for the distribution.

In many engineering applications, one is interested in structures with elastic properties which undergo deformation due to external loads. This interest has motivated a deep study of the equations underlying the deformation and how to solve them during the two last centuries. In this thesis, we propose a method that allows us to construct exact solutions to these equations. We prove that the partial differential equation governing the deformation is equivalent to the well-studied Cauchy-Riemann equation on the unit disk. Furthermore, we prove sufficient conditions for when the exact solutions to the Cauchy-Riemann equation on the unit disk can be used to construct solutions to the physical problem. We end the thesis by outlining a method for solving the elasticity equation in a general simply connected domain with a known conformal mapping to the unit disk. This method simplifies the formulas of Kolosov and Muskhelishvili, which are constructed by complex potentials in a similar, but more indirect way. It also allows us to obtain solutions in domains where standard numerical methods, such as e.g. the finite element method, proves difficult or even impossible to apply.

This bachelor's thesis discusses from an ergodic-theoretical perspective the "metric functional analysis" that Anders Karlsson and others have developed in the recent years. We introduce a new symbolic calculus for metric functionals which includes a notion of the adjoint of a nonexpansive map. Using these tools we revisit many central results, including Karlsson's spectral principle and its stronger form for star-shaped spaces due to Gaubert and Vigeral, as well as the multiplicative ergodic theorem of Karlsson-Ledrappier.

Markov chain is a mathematical tool for modeling systems that evolve over time and hasbeen used in many fields such as physics, chemistry, economics, biology, and data science.This thesis contains an introduction to the theory and the applications of Markov chains,focusing on those with finite state spaces. Starting with basic concepts and techniques, thetheory of Markov chains is comprehensively studied. The basic concepts covered includethe Markov property, transition matrix, higher order transition probabilities, classification of states, and Markov chains as graphs. The stationary distribution, its importancein probability theory, existence, and uniqueness of stationary distribution are then discussed, while the final part of the thesis deals with the simulations of Markov chains. Twoexamples are presented to illustrate the technique of Markov chain simulation, includinga weather prediction model and a DNA sequence model.

In this thesis a method for generating option portfolios using machine learning, more specifically WGAN-GP (Wasserstein Generative Adversarial Networks with Gradient Penalty), is presented. To reduce the complexity however, the model does not immediately generate portfolios with option series, but instead option classes, which includes the underlying asset, option type and direction of position. The generated portfolios are then transformed such that they include option series. A comparison between the real and generated portfolios was conducted, using a range of different metrics, such as number of positions, total market value and margin. Which concluded in that the model, presented in this thesis, effectively functions as a portfolio generator.

<p>In this thesis, which consists of five papers (A,B,C,D,E), we are interested in questions related to quadrature domains. Among the problems studied are the possibility of changing the type of measure in a quadrature identity (from complex to real and from real signed to positive), properties of partial balayage, which in a sense can be used to generate quadrature domains, and mother bodies which are closely related to inversion of partial balayage.</p><p>These three questions are discussed in papers A,D respectively B.</p><p>The first of these questions (when trying to go from real signed to positive measures) leads to the study of approximation in the cone of positive harmonic functions. These questions are closely related to properties of the harmonic measure on the Martin boundary, and this relationship leads to the study of harmonic measures on ideal boundaries in paper E. Some other approaches to the same problem also lead to some extent to the study of properties of classical balayage in paper C.</p>

Research has shown that the mathematics textbooks are the most widely used in Swedish schools, compared to textbooks in other subjects. At the same time, studies have shown that the content of the textbooks do not fulfil the goals presented in the national education steering documents regarding problem solving in math. The purpose of this study is to analyze textbooks and corresponding teacher’s guide in mathematics for the second grade. Starting from a didactic perspective as an approach to problem solving in order to analyze the teaching material, I decided to use the analytical model constructed by Ann Kristin Larsen. In order to conduct the study, the following questions have been used in this study: In what way the problem solving has been presented in the textbooks? Which problem solving strategies are presented in respective teaching material based on didactic perspective? What types of problem solving tasks are presented in respective teaching material?  In what way the concept problem solving is presented in the teacher’s guide? In conclusion, the result of the study shows that there are both similarities and differences between the two instructional materials that have been studied in the way they presented problem solving. The study shows that the teaching material is not compatible with Charles and Lester’s (1982) criteria. As for the teacher's guide and the support it provides, the investigation shows that different textbooks give different support and guidance to teachers.

The main purpose of this project was to help Swedbank get a better understandingof how gross domestic product growth rate develops in the future froma data set of macroeconomic variables. Since GDP values are released long aftera quarter has ended Swedbank would like to have a model that could predictupcoming GDP from these data sets. This was solved by a combination ofgrowth rate predictions from a dynamic factor model, a vector autoregressivemodel and two machine learning models. The predictions were combined usinga weighting method called system averaging model where the model predictionwith least historical error receives the largest weight in the nal future prediction.In previous work a simple moving average model has been implementedto achieve this eect however there are several aws in a simple moving averagemodel. Most of these defects could in theory be avoided by using an exponentialweighting scheme instead. This resulted in the use of an exponentialweighting method that is used to calculate weights for future predictions. Themain conclusions from this project were that some predictions could get betterwhen removing bad performing models which had too large of a weight. Puttingtoo high weight on a single well performing model is also not optimal since thepredictions could get very unstable because of varying model performance. Theexponential weighting scheme worked well for some predictions however whenthe parameter , that controls how the weight is distributed between recent andhistorical errors, got too small a problem arose. Too few values were used toform the nal weights for the prediction and the estimate got unsteady results.

In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε &gt; 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented. / STINT (DD2017-6936) "Mathematics Bachelor Program for Efficient Computations"