Strategisten reaalioptioiden mallintaminen Monte Carlo -simulointimenetelmällä, case Voest Alpine Stahl Ag

Tutkielman päätavoitteena oli selvittää, miten Monte Carlo –simulointi soveltuu strategisten reaalioptioiden arvonmääritykseen. Tutkielman teoriaosuudessa käytiin läpi reaalioptioteoriaa ja Monte Carlo –simulointimenetelmää toiminta-analyyttisella tutkimusotteella. Tuloksena todettiin, että simulointimenetelmää on reaalioptioiden yhteydessä yleensä käytetty, kun muu menetelmä ei ole ollut mahdollinen. Tutkielman pääpaino on tapaustutkimukseen pohjautuvassa empiriaosuudessa, jossa rakennettiin päätöksentekometodologista tutkimusotetta seuraten simulointimalli, jolla tutkittiin Voest Alpine Stahl Ag:n vaihtoehtoisten hinnoittelustrategioiden taloudellista vaikutusta. Mallin rakentaminen perustui yrityksen tilinpäätösaineistoon. Havaittiin, ettei yritys ole valitsemansa strategian vuoksi juurikaan menettänyt tuottoja, mutta toisaalta pelkkä tilinpäätösaineisto ei riitä kovin luotettavaan tarkasteluun. Vuosikertomusten antaman tiedon pohjalta analysoitiin lisäksi yrityksen toiminnassa havaittuja reaalioptioita. Monte Carlo –simulointimenetelmä sopii reaalioptioiden arvonmääritykseen, mutta kriittisiä tekijöitä ovat mallin rakentaminen ja lähtötietojen oikeellisuus. Numeerisen mallin rinnalla on siksi aiheellista suorittaa myös laadullista reaalioptioanalyysia.

Monte Carlo Hypothesis Testing with The Sharpe Ratio

The purpose of this master thesis was to perform simulations that involve use of random number while testing hypotheses especially on two samples populations being compared weather by their means, variances or Sharpe ratios. Specifically, we simulated some well known distributions by Matlab and check out the accuracy of an hypothesis testing. Furthermore, we went deeper and check what could happen once the bootstrapping method as described by Effrons is applied on the simulated data. In addition to that, one well known RobustSharpe hypothesis testing stated in the paper of Ledoit and Wolf was applied to measure the statistical significance performance between two investment founds basing on testing weather there is a statistically significant difference between their Sharpe Ratios or not. We collected many literatures about our topic and perform by Matlab many simulated random numbers as possible to put out our purpose; As results we come out with a good understanding that testing are not always accurate; for instance while testing weather two normal distributed random vectors come from the same normal distribution. The Jacque-Berra test for normality showed that for the normal random vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal distribution in contrast 5,3% and 4,3% failed to shown the truth already known; but when we introduce the bootstrapping methods by Effrons while estimating pvalues where the hypothesis decision is based, the accuracy of the test was 100% successful. From the above results the reports showed that bootstrapping methods while testing or estimating some statistics should always considered because at most cases the outcome are accurate and errors are minimized in the computation. Also the RobustSharpe test which is known to use one of the bootstrapping methods, studentised one, were applied first on different simulated data including distribution of many kind and different shape secondly, on real data, Hedge and Mutual funds. The test performed quite well to agree with the existence of statistical significance difference between their Sharpe ratios as described in the paper of Ledoit andWolf.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Monte Carlo -reaktorifysiikkalaskennan ja laskennallisen virtausmekaniikan kytkentä kuulakekoreaktorissa

Monte Carlo -reaktorifysiikkakoodit nykyisin käytettävissä olevilla laskentatehoilla tarjoavat mielenkiintoisen tavan reaktorifysiikan ongelmien ratkaisuun. Neljännen sukupolven ydinreaktoreissa käytettävät uudet rakenteet ja materiaalit ovat haasteellisia nykyisiin reaktoreihin suunnitelluille laskentaohjelmille. Tässä työssä Monte Carlo -reaktorifysiikkakoodi ja CFD-koodi yhdistetään kytkettyyn laskentaan kuulakekoreaktorissa, joka on yksi korkealämpötilareaktorityyppi. Työssä käytetty lähestymistapa on uutta maailmankin mittapuussa ajateltuna.

Structural modelling of liquid ZrO2 and glassy B2O3 by using AB INITIO Molecular Dynamics method

Atomic structure of ZrO2 and B2O3 was investigated in this work. New data under extreme conditions (T = 3100 K) was obtained for the liquid ZrO2 structure. A fractional number of boron was investigated for glassy structure of B2O3. It was shown that it is possible to obtain an agreement for the fractional number between NMR and DFT techniques using a suitable initial configuration.

Statistical Analysis and Numerics of Heat Exchanger Models

The identifiability of the parameters of a heat exchanger model without phase change was studied in this Master’s thesis using synthetically made data. A fast, two-step Markov chain Monte Carlo method (MCMC) was tested with a couple of case studies and a heat exchanger model. The two-step MCMC-method worked well and decreased the computation time compared to the traditional MCMC-method. The effect of measurement accuracy of certain control variables to the identifiability of parameters was also studied. The accuracy used did not seem to have a remarkable effect to the identifiability of parameters. The use of the posterior distribution of parameters in different heat exchanger geometries was studied. It would be computationally most efficient to use the same posterior distribution among different geometries in the optimisation of heat exchanger networks. According to the results, this was possible in the case when the frontal surface areas were the same among different geometries. In the other cases the same posterior distribution can be used for optimisation too, but that will give a wider predictive distribution as a result. For condensing surface heat exchangers the numerical stability of the simulation model was studied. As a result, a stable algorithm was developed.

Novel force control methods in a teleoperation system of a hydraulic slider

The objective of the this research project is to develop a novel force control scheme for the teleoperation of a hydraulically driven manipulator, and to implement an ideal transparent mapping between human and machine interaction, and machine and task environment interaction. This master‘s thesis provides a preparatory study for the present research project. The research is limited into a single degree of freedom hydraulic slider with 6-DOF Phantom haptic device. The key contribution of the thesis is to set up the experimental rig including electromechanical haptic device, hydraulic servo and 6-DOF force sensor. The slider is firstly tested as a position servo by using previously developed intelligent switching control algorithm. Subsequently the teleoperated system is set up and the preliminary experiments are carried out. In addition to development of the single DOF experimental set up, methods such as passivity control in teleoperation are reviewed. The thesis also contains review of modeling of the servo slider in particular reference to the servo valve. Markov Chain Monte Carlo method is utilized in developing the robustness of the model in presence of noise.

Neutronisäteilylle altistuminen käytetyn polttoaineen siirrossa Olkiluodon voimalaitoksella

Tässä työssä on tutkittu OL1/OL2-ydinvoimalaitosten käytetyn polttoaineen siirrossa aiheutuvaa altistusta neutronisäteilylle. Käytetty polttoaine siirretään vedellä täytetyssä käytetyn polttoaineen siirtosäiliössä Castor TVO:ssa OL1/OL2-laitoksilta käytetyn polttoaineen varastolle. Siirtotyön aikana useat eri ammattiryhmiin kuuluvat henkilöt työskentelevät siirtosäiliön välittömässä läheisyydessä, altistuen käytetystä polttoaineesta emittoituvalle fotoni- ja neutronisäteilylle. Aikaisemmista neutronisäteilyannosten mittauksista on todettu, ettei jatkuvalle altistuksen seurannalle ole ollut tarvetta. Tämän työn tarkoitus on selvittää teoreettisilla laskelmilla siirtotyöhön osallistuvan henkilön mahdollisuus saada kirjausrajan ylittävä annos neutronisäteilyä. Neutronisäteilyn annosnopeudet siirtosäiliötä ympäröivässä tilassa on laskettu yhdysvaltalaisella Monte Carlo-menetelmään perustuvalla MCNP-ohjelmalla. MCNP:llä mallinnettiin siirtosäiliö, siirtosäiliön sisältämä polttoaine ja ympäröivä tila kolmella jäähtymisajalla ja kolmella keskimääräisellä maksimipoistopalamalla. Polttoainenippujen isotooppikonsentraatiot ja säteilylähteiden voimakkuudet on laskettu Studsvik SNF-ohjelmalla. Simuloinnin perusteella voidaan todeta, ettei neutronisäteilyannosten jatkuvalle seurannalle ole tarvetta käytetyn polttoaineen siirrossa. Vaikka neutronisäteilyn annosnopeudet voivat nousta siirtosäiliön läheisyydessä suhteellisen suuriksi, ovat siirtosäiliön lähellä tehtävät työt niin lyhytaikaisia, että kirjausrajan ylitystä voidaan pitää hyvin epätodennäköisenä. Johtopäätökset varmistetaan työssä suunnitellulla mittausjärjestelyllä.

Inverting ionospheric D-region electron density pro-file from riometer measurement

The aim of this work is to invert the ionospheric electron density profile from Riometer (Relative Ionospheric opacity meter) measurement. The newly Riometer instrument KAIRA (Kilpisjärvi Atmospheric Imaging Receiver Array) is used to measure the cosmic HF radio noise absorption that taking place in the D-region ionosphere between 50 to 90 km. In order to invert the electron density profile synthetic data is used to feed the unknown parameter Neq using spline height method, which works by taking electron density profile at different altitude. Moreover, smoothing prior method also used to sample from the posterior distribution by truncating the prior covariance matrix. The smoothing profile approach makes the problem easier to find the posterior using MCMC (Markov Chain Monte Carlo) method.

Public-private partnership investments in dry ports – Russian logistics markets and risks

The investments have always been considered as an essential backbone and so-called ‘locomotive’ for the competitive economies. However, in various countries, the state has been put under tight budget constraints for the investments in capital intensive projects. In response to this situation, the cooperation between public and private sector has grown based on public-private mechanism. The promotion of favorable arrangement for collaboration between public and private sectors for the provision of policies, services, and infrastructure in Russia can help to address the problems of dry ports development that neither municipalities nor the private sector can solve alone. Especially, the stimulation of public-private collaboration is significant under the exposure to externalities that affect the magnitude of the risks during all phases of project realization. In these circumstances, the risk in the projects also is becoming increasingly a part of joint research and risk management practice, which is viewed as a key approach, aiming to take active actions on existing global and specific factors of uncertainties. Meanwhile, a relatively little progress has been made on the inclusion of the resilience aspects into the planning process of a dry ports construction that would instruct the capacity planner, on how to mitigate the occurrence of disruptions that may lead to million dollars of losses due to the deviation of the future cash flows from the expected financial flows on the project. The current experience shows that the existing methodological base is developed fragmentary within separate steps of supply chain risk management (SCRM) processes: risk identification, risk evaluation, risk mitigation, risk monitoring and control phases. The lack of the systematic approach hinders the solution of the problem of risk management processes of dry port implementation. Therefore, management of various risks during the investments phases of dry port projects still presents a considerable challenge from the practical and theoretical points of view. In this regard, the given research became a logical continuation of fundamental research, existing in the financial models and theories (e.g., capital asset pricing model and real option theory), as well as provided a complementation for the portfolio theory. The goal of the current study is in the design of methods and models for the facilitation of dry port implementation through the mechanism of public-private partnership on the national market that implies the necessity to mitigate, first and foremost, the shortage of the investments and consequences of risks. The problem of the research was formulated on the ground of the identified contradictions. They rose as a continuation of the trade-off between the opportunities that the investors can gain from the development of terminal business in Russia (i.e. dry port implementation) and risks. As a rule, the higher the investment risk, the greater should be their expected return. However, investors have a different tolerance for the risks. That is why it would be advisable to find an optimum investment. In the given study, the optimum relates to the search for the efficient portfolio, which can provide satisfaction to the investor, depending on its degree of risk aversion. There are many theories and methods in finance, concerning investment choices. Nevertheless, the appropriateness and effectiveness of particular methods should be considered with the allowance of the specifics of the investment projects. For example, the investments in dry ports imply not only the lump sum of financial inflows, but also the long-term payback periods. As a result, capital intensity and longevity of their construction determine the necessity from investors to ensure the return on investment (profitability), along with the rapid return on investment (liquidity), without precluding the fact that the stochastic nature of the project environment is hardly described by the formula-based approach. The current theoretical base for the economic appraisals of the dry port projects more often perceives net present value (NPV) as a technique superior to other decision-making criteria. For example, the portfolio theory, which considers different risk preference of an investor and structures of utility, defines net present value as a better criterion of project appraisal than discounted payback period (DPP). Meanwhile, in business practice, the DPP is more popular. Knowing that the NPV is based on the assumptions of certainty of project life, it cannot be an accurate appraisal approach alone to determine whether or not the project should be accepted for the approval in the environment that is not without of uncertainties. In order to reflect the period or the project’s useful life that is exposed to risks due to changes in political, operational, and financial factors, the second capital budgeting criterion – discounted payback period is profoundly important, particularly for the Russian environment. Those statements represent contradictions that exist in the theory and practice of the applied science. Therefore, it would be desirable to relax the assumptions of portfolio theory and regard DPP as not fewer relevant appraisal approach for the assessment of the investment and risk measure. At the same time, the rationality of the use of both project performance criteria depends on the methods and models, with the help of which these appraisal approaches are calculated in feasibility studies. The deterministic methods cannot ensure the required precision of the results, while the stochastic models guarantee the sufficient level of the accuracy and reliability of the obtained results, providing that the risks are properly identified, evaluated, and mitigated. Otherwise, the project performance indicators may not be confirmed during the phase of project realization. For instance, the economic and political instability can result in the undoing of hard-earned gains, leading to the need for the attraction of the additional finances for the project. The sources of the alternative investments, as well as supportive mitigation strategies, can be studied during the initial phases of project development. During this period, the effectiveness of the investments undertakings can also be improved by the inclusion of the various investors, e.g. Russian Railways’ enterprises and other private companies in the dry port projects. However, the evaluation of the effectiveness of the participation of different investors in the project lack the methods and models that would permit doing the particular feasibility study, foreseeing the quantitative characteristics of risks and their mitigation strategies, which can meet the tolerance of the investors to the risks. For this reason, the research proposes a combination of Monte Carlo method, discounted cash flow technique, the theory of real options, and portfolio theory via a system dynamics simulation approach. The use of this methodology allows for comprehensive risk management process of dry port development to cover all aspects of risk identification, risk evaluation, risk mitigation, risk monitoring, and control phases. A designed system dynamics model can be recommended for the decision-makers on the dry port projects that are financed via a public-private partnership. It permits investors to make a decision appraisal based on random variables of net present value and discounted payback period, depending on different risks factors, e.g. revenue risks, land acquisition risks, traffic volume risks, construction hazards, and political risks. In this case, the statistical mean is used for the explication of the expected value of the DPP and NPV; the standard deviation is proposed as a characteristic of risks, while the elasticity coefficient is applied for rating of risks. Additionally, the risk of failure of project investments and guaranteed recoupment of capital investment can be considered with the help of the model. On the whole, the application of these modern methods of simulation creates preconditions for the controlling of the process of dry port development, i.e. making managerial changes and identifying the most stable parameters that contribute to the optimal alternative scenarios of the project realization in the uncertain environment. System dynamics model allows analyzing the interactions in the most complex mechanism of risk management process of the dry ports development and making proposals for the improvement of the effectiveness of the investments via an estimation of different risk management strategies. For the comparison and ranking of these alternatives in their order of preference to the investor, the proposed indicators of the efficiency of the investments, concerning the NPV, DPP, and coefficient of variation, can be used. Thus, rational investors, who averse to taking increased risks unless they are compensated by the commensurate increase in the expected utility of a risky prospect of dry port development, can be guided by the deduced marginal utility of investments. It is computed on the ground of the results from the system dynamics model. In conclusion, the outlined theoretical and practical implications for the management of risks, which are the key characteristics of public-private partnerships, can help analysts and planning managers in budget decision-making, substantially alleviating the effect from various risks and avoiding unnecessary cost overruns in dry port projects.

Mobile robot localization using sonar ranging and wlan intensity maps

 Main goal of this thesis was to implement a localization system which uses sonars and WLAN intensity maps to localize an indoor mobile robot. A probabilistic localization method, Monte Carlo Localization is used in localization. Also the theory behind probabilistic localization is explained. Two main problems in mobile robotics, path tracking and global localization, are solved in this thesis. Implemented system can achieve acceptable performance in path tracking. Global localization using WLAN received signal strength information is shown to provide good results, which can be used to localize the robot accurately, but also some bad results, which are no use when trying to localize the robot to the correct place. Main goal of solving ambiguity in office like environment is achieved in many test cases.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Modeling reaction kinetics and mass transfer in ozonation in water solutions

This dissertation is based on four articles dealing with modeling of ozonation. The literature part of this considers some models for hydrodynamics in bubble column simulation. A literature review of methods for obtaining mass transfer coefficients is presented. The methods presented to obtain mass transfer are general models and can be applied to any gas-liquid system. Ozonation reaction models and methods for obtaining stoichiometric coefficients and reaction rate coefficients for ozonation reactions are discussed in the final section of the literature part. In the first article, ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. A more general method for estimation of mass transfer and Henry’s coefficient was developed from the Beltrán method. The ozone volumetric mass transfer coefficient and the Henry’s coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A minor dependence of the Henry’s law constant on pH was detected at the pH range 4 - 9. In the second article, a new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semi-batch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with the literature data. The reaction order in the pH range 7-10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. Sensitivity analysis was conducted using object function method to obtain information about the reliability and identifiability of the estimated parameters. In the third article, the reaction rate coefficients and the stoichiometric coefficients in the reaction of ozone with the model component p-nitrophenol were estimated at low pH of water using nonlinear optimization. A novel method for estimation of multireaction model parameters in ozonation was developed. In this method the concentration of unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the p-nitrophenol decomposition rate on the pathway producing 4- nitrocatechol. In the fourth article, the reaction kinetics of p-nitrophenol ozonation was studied in a bubble column at pH 2. Using the new reaction kinetic model presented in the previous article, the reaction kinetic parameters, rate coefficients, and stoichiometric coefficients as well as the mass transfer coefficient were estimated with nonlinear estimation. The decomposition rate of pnitrophenol was found to be equal both on the pathway producing hydroquinone and on the path way producing 4-nitrocathecol. Comparison of the rate coefficients with the case at initial pH 5 indicates that the p-nitrophenol degradation producing 4- nitrocathecol is more selective towards molecular ozone than the reaction producing hydroquinone. The identifiability and reliability of the estimated parameters were analyzed with the Marcov chain Monte Carlo (MCMC) method. @All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author.