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581	Equilibrium Strategies for Time-Inconsistent Stochastic Optimal Control of Asset Allocation / Jämviktsstrategier för tidsinkonsistent stokastisk optimal styrning av tillgångsallokering Dimitry El Baghdady, Johan January 2017 (has links) We have examinined the problem of constructing efficient strategies for continuous-time dynamic asset allocation. In order to obtain efficient investment strategies; a stochastic optimal control approach was applied to find optimal transaction control. Two mathematical problems are formulized and studied: Model I; a dynamic programming approach that maximizes an isoelastic functional with respect to given underlying portfolio dynamics and Model II; a more sophisticated approach where a time-inconsistent state dependent mean-variance functional is considered. In contrast to the optimal controls for Model I, which are obtained by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation; the efficient strategies for Model II are constructed by attaining subgame perfect Nash equilibrium controls that satisfy the extended HJB equation, introduced by Björk et al. in [1]. Furthermore; comprehensive execution algorithms where designed with help from the generated results and several simulations are performed. The results reveal that optimality is obtained for Model I by holding a fix portfolio balance throughout the whole investment period and Model II suggests a continuous liquidation of the risky holdings as time evolves. A clear advantage of using Model II is concluded as it is far more efficient and actually takes time-inconsistency into consideration. / Vi har undersökt problemet som uppstår vid konstruktion av effektiva strategier för tidskontinuerlig dynamisk tillgångsallokering. Tillvägagångsättet för konstruktionen av strategierna har baserats på stokastisk optimal styrteori där optimal transaktionsstyrning beräknas. Två matematiska problem formulerades och betraktades: Modell I, en metod där dynamisk programmering används för att maximera en isoelastisk funktional med avseende på given underliggande portföljdynamik. Modell II, en mer sofistikerad metod som tar i beaktning en tidsinkonsistent och tillståndsberoende avvägning mellan förväntad avkastning och varians. Till skillnad från de optimala styrvariablerna för Modell I som satisfierar Hamilton-Jacobi-Bellmans (HJB) partiella differentialekvation, konstrueras de effektiva strategierna för Modell II genom att erhålla subgame perfekt Nashjämvikt. Dessa satisfierar den utökade HJB ekvationen som introduceras av Björk et al. i [1]. Vidare har övergripande exekveringsalgoritmer skapats med hjälp av resultaten och ett flertal simuleringar har producerats. Resultaten avslöjar att optimalitet för Modell I erhålls genom att hålla en fix portföljbalans mellan de riskfria och riskfyllda tillgångarna, genom hela investeringsperioden. Medan för Modell II föreslås en kontinuerlig likvidering av de riskfyllda tillgångarna i takt med, men inte proportionerligt mot, tidens gång. Slutsatsen är att det finns en tydlig fördel med användandet av Modell II eftersom att resultaten påvisar en påtagligt högre grad av effektivitet samt att modellen faktiskt tar hänsyn till tidsinkonsistens. Stochastic optimal control dynamic programming asset allocation non-cooperative games subgame perfect Nash equilibrium time-inconsistency dynamic portfolio optimization mean-variance state dependent risk aversion extended Hamilton-Jacobi-Bellman execution algorithms. Stokastisk optimal styrning dynamisk programmering tillgångsallokering icke-kooperativa spel Nashjämvikt tidsinkonsistens dynamisk portföljoptimering tillståndsberoende riskhantering utökad Hamilton-Jacobi- Computational Mathematics Beräkningsmatematik
582	Designing Effective Derivative Line Filters: Utilizing convolution to extract extra information / Utformning av effektiva derivata-linjefilter: Användning av faltning för att extrahera extra information Lorentzon, Gustaf January 2023 (has links) The ability to generate accurate approximations of derivatives holds significant importance in numerous scientific fields, including chemistry, economics and fluid mechanics. This thesis is centred around extracting hidden information in data using Smoothness-Increasing Accuracy-Conserving (SIAC) filters. The target application is in calculating derivatives in simulations of fluid flow. SIAC filters are based on convolution. Because of the properties used to construct the convolution kernel, we are able to design post-processing filters that can extract extra derivative information with high accuracy. In the past, these filters have typically had a tensor-product structure, which requires multi-dimensional filtering. Because of this, the filtering process can be very computationally expensive. The goal of this thesis is to develop one-dimensional line filters that are able to extract the derivative information more efficiently. By utilizing line filters, we aim to significantly cut the computational cost of the filtering process, while also maintaining the high accuracy. / Att kunna generera approximeringar av derivator med hög noggrannhet har stor användning inom många vetenskapliga områden, inklusive kemi, ekonomi och strömningsmekanik. Denna uppsats är fokuserad på att extrahera dold information i data med hjälp av en specifik typ av faltningsfilter. Dessa filter kan öka kontinuitetsgraden av data utan att minska noggrannheten. Den avsedda tilläpningen för dessa filter är inom strömningsmekanik, framförallt beräkning av derivator i flöden. Tack vare egenskaperna som används för att konstruera faltningskärnan kan vi utforma efterbehandlingsfilter som kan extrahera derivatainformation med hög noggrannhet. Tidigare har dessa filter ofta haft en tensorproduktstruktur, vilket kräver flerdimensionell filtrering. På grund av detta har filtreringen ofta en hög beräkningskostnad. Målet med denna uppsats är att utveckla endimensionella linjefilter som kan extrahera derivatainformation mer effektivt. Syftet är att använda dessa linjefilter för att betydligt miska filtreringens beräkningskostnad och samtidigt behålla den höga noggrannheten. Computational Fluid Dynamics Convolution Filters Convolution Kernels Derivatives Extracting Extra Accuracy Filtration Post-processing Signal-processing Visualization Vorticity Beräkningsbaserad Strömningsdynamik Faltningsfilter Faltningskärnor Derivator Extrahering av Extra Noggrannhet Filtrering Efterbehandling Kontinuitetsökande Noggrannhetsbevarande Signalbehandling Visualisering Vorticitet Computational Mathematics Beräkningsmatematik
583	Terrain Modeling in Dynamic Atmosphere for a Ground Wave Propagation Simulator Karlsen, Gustaf January 2024 (has links) The parabolic equation methods are advantageous in simulating under small time frames because of their low computational complexity. Because of this they are also feasible to implement on low end hardware. Due to the parabolic approximation they are based on, much work exists on improving the error introduced from the approximation. In this publication, further effort is put into developing these methods and the result from a master thesis at Tietoevry are presented. An in-house algorithm for evaporation duct propagation has been altered to improve the terrain modeling and to include range varying refractivity in a split step Fourier method called the discrete mixed Fourier transform. Previously only the piecewise linear shift map was utilized for terrain modeling which is known to become unstable at propagation angles exceeding around 15 degrees from the horizontal. By utilizing a hybrid method between piecewise linear shift map and knife edge method the stability issues are partially avoided, hence the solutions generated with the hybrid method are stable for a larger range of slope angles than with only using piecewise linear shift map. The range varying refractivity was included in the discrete mixed fourier transform by indexing making it possible to simulate dynamic evaporation duct heights. The report starts with a review of the theoretical foundation that the algorithm is built upon. Secondly, a logical list of steps outlines the altered algorithm. To conclude, the changes to the code are presented and discussed with the new results together with remarks on possible future improvements and current problems with the algorithm. electromagnetic wave propagation UHF ground troposphere evaporation telecom duct radio link 5G terrain modeling refractivity index curves split step fourier methods discrete mixed fourier transform numerical physics elektromagnetisk våg propagering mark telekommunikation vågor 5g terräng modellering transform numeriska metoder fysik telekom Telecommunications Telekommunikation Signal Processing Signalbehandling Communication Systems Kommunikationssystem Computational Mathematics Beräkningsmatematik
584	Probabilistic Multidisciplinary Design Optimization on a high-pressure sandwich wall in a rocket engine application Wahlström, Dennis January 2017 (has links) A need to find better achievement has always been required in the space industrythrough time. Advanced technologies are provided to accomplish goals for humanityfor space explorer and space missions, to apprehend answers and widen knowledges. These are the goals of improvement, and in this thesis, is to strive and demandto understand and improve the mass of a space nozzle, utilized in an upperstage of space mission, with an expander cycle engine. The study is carried out by creating design of experiment using Latin HypercubeSampling (LHS) with a consideration to number of design and simulation expense.A surrogate model based optimization with Multidisciplinary Design Optimization(MDO) method for two different approaches, Analytical Target Cascading (ATC) and Multidisciplinary Feasible (MDF) are used for comparison and emend the conclusion. In the optimization, three different limitations are being investigated, designspace limit, industrial limit and industrial limit with tolerance. Optimized results have shown an incompatibility between two optimization approaches, ATC and MDF which are expected to be similar, but for the two limitations, design space limit and industrial limit appear to be less agreeable. The ATC formalist in this case dictates by the main objective, where the children/subproblems only focus to find a solution that satisfies the main objective and its constraint. For the MDF, the main objective function is described as a single function and solved subject to all the constraints. Furthermore, the problem is not divided into subproblems as in the ATC. Surrogate model based optimization, its solution influences by the accuracy ofthe model, and this is being investigated with another DoE. A DoE of the full factorial analysis is created and selected to study in a region near the optimal solution.In such region, the result has evidently shown to be quite accurate for almost allthe surrogate models, except for max temperature, damage and strain at the hottestregion, with the largest common impact on inner wall thickness of the space nozzle. Results of the new structure of the space nozzle have shown an improvement of mass by ≈ 50%, ≈ 15% and ≈ -4%, for the three different limitations, design spacelimit, industrial limit and industrial limit with tolerance, relative to a reference value,and ≈ 10%, ≈ 35% and ≈ 25% cheaper to manufacture accordingly to the defined producibility model. Multidisciplinary Design Optimization Analytical Target Cascading Multidisciplinary Feasible Space Nozzle Ariane Expander Cycle Engine Upper stage space rocket engine Probabilistic Augmented Lagrangian relaxation Finite element Solid Mechanics Thermodynamics Aerodynamics Industrial approach Latin Hypercube Sampling Factorial Analysis Analysis of Variance Other Physics Topics Annan fysik Aerospace Engineering Rymd- och flygteknik Probability Theory and Statistics Sannolikhetsteori och statistik Vehicle Engineering Farkostteknik Reliability and Maintenance Tillförlitlighets- och kvalitetsteknik Applied Mechanics Teknisk mekanik Computational Mathematics Beräkningsmatematik Fluid Mechanics and Acoustics Strömningsmekanik och akustik
585	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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