In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In considering a slightly more complicated model over a finite probability space, we see that Q once again makes its appearance. Finally, in the context of continuous time, we build a framework of stochastic calculus to model the trajectories of asset prices on a finite time interval. Under the absence of arbitrage once more, we see that Q makes its return as a Radon-Nikodym derivative of our initial probability measure. Finally, we use the properties of Q and a stochastic differential equation that models the dynamics of the assets of our market, known as the Ito formula, in order to derive the classic Black-Scholes Equation.

Masters of Commerce / If share price fluctuations follow a simple random walk then it implies that forecasting models based on historical growth rates have little ability to forecast acceptable share price movements over a certain period. The simple random walk description of share price dynamics is obtained when a large number of investors have equal probability to buy or sell based on their own opinion. This simple random walk description of the stock market is in essence the Efficient Market Hypothesis, EMT. EMT is the central concept around which financial modelling is based which includes the Black-Scholes model and other important theoretical underpinnings of capital market theory like mean-variance portfolio selection, arbitrage pricing theory (APT), security market line and capital asset pricing model (CAPM). These theories, which postulates that risk can be reduced to zero sets the foundation for option pricing and is a key component in financial software packages used for pricing and forecasting in the financial industry. The model used by Black and Scholes and other models mentioned above are Gaussian, i.e. they exhibit a random nature. This Gaussian property and the existence of expected returns and continuous time paths (also Gaussian properties) allow the use of stochastic calculus to solve complex Black- Scholes models. However, if the markets are not Gaussian then the idea that risk can be. (educed to zero can lead to a misleading and potentially disastrous sense of security on the financial markets. This study project test the null hypothesis - share prices on the JSE follow a random walk - by means of graphical techniques such as symmetry plots and Quantile-Quantile plots to analyse the test distributions. In both graphical techniques evidence for the rejection of normality was found. Evidenceleading to the rejection of the hypothesis was also found through nonparametric or distribution free methods at a 1% level of significance for Anderson-Darling and Runs test.

The increasing demand for renewable energy sources to meet climate targets and reduce carbon emissions poses challenges to the power grid due to their intermittent nature. One potential solution to maintain grid stability is by implementing Hybrid Energy Systems (HESs) that incorporate a Battery Energy Storage System (BESS). To achieve the most favorable outcome in terms of both technical feasibility and profitability of a BESS, it is essential to employ models for simulating and optimizing the control of system components. This thesis focuses on the analysis of energy and revenue streams in a HES consisting of a BESS, photovoltaics (PVs), and an energy load including a fast charging station for electric vehicles (EVs). The objective is to optimize the system based on revenue generation by comparing the control techniques of peak shaving, energy arbitrage, and the integration of ancillary services within the Swedish energy market. The research questions explore the optimal utilization of the BESS and assess the impact of the different control techniques. A model is created in Python with the package CasADi where data from an ongoing installation of a HES in southern Sweden is combined with data from literature research. The model includes an objective function that minimizes the total cost of power from the grid based on the day-ahead price, battery degradation, and monthly peak power.  To answer the research questions, four different scenarios are simulated. The first scenario is a base for comparison, the second one focuses on peak shaving and energy arbitrage, the third on participation in the ancillary service FCR-D upwards regulation, and the last one is a combination of peak shaving, energy arbitrage, and the ancillary service FCR-D. The results show that the remuneration from the ancillary service FCR-D is comparably much higher than the revenues generated from peak shaving and energy arbitrage, providing more than 500% of revenue compared to the same system but without a BESS. The scenario with peak shaving and energy arbitrage shows an increase in revenue of 29% but with more cycling of the battery which could cause losses in performance in the long term. To validate the results, sensitivity analyses are conducted by evaluating weighting in the objective function, implementing Model Predictive Control (MPC), and reviewing price variations.  In conclusion, efficient control techniques can enhance system performance, minimize losses, and ensure optimal utilization of different energy sources, leading to improved feasibility and profitability. The optimal usage of a BESS involves finding a balance between maximizing revenue generation and minimizing battery degradation. This can be achieved through control strategies that optimize the charging and discharging patterns of the BESS based on electricity price signals, demand patterns, and battery health considerations.

В данной работе исследуется влияние типов предпринимательства на экономический рост. В рамках синергетического эффекта рыночно-ориентированной реформы рассматривается влияние типов предпринимательства на экономический рост и выдвигаются соответствующие предложения по политике государства в рамках поддержки предпринимательства в КНР. Цель работы – исследование роли предпринимательства в развитии экономики КНР и разработка предложений по развитию предпринимательской деятельности в Китае. Новизна исследования заключается в том, что получены и обоснованы экономико-статистические оценки влияния предпринимательства на экономический рост КНР, а также предложен алгоритм поведения для развития предпринимательской деятельности в Китае с учетом особенностей исследованных типов предпринимательства. / This paper examines the impact of types of entrepreneurship on economic growth. As part of the synergistic effect of the market-oriented reform, the influence of types of entrepreneurship on economic growth is considered and relevant proposals are put forward for state policy in the framework of supporting entrepreneurship in the PRC. The purpose of the work is to study the role of entrepreneurship in the development of the PRC economy and develop proposals for the development of entrepreneurial activity in China. The novelty of the study lies in the fact that economic and statistical estimates of the impact of entrepreneurship on the economic growth of China have been obtained and substantiated, and an algorithm of behavior for the development of entrepreneurial activity in China has been proposed, taking into account the characteristics of the studied types of entrepreneurship.

The rise of cryptocurrencies has brought with it new math problems with new sets of constraints. The MEV problem entails solving for the ordering of pending trades that maximizes a block creator's profit. In decentralized finance, time is a big constraint, so an exhaustive search of all possible orderings is impossible. I propose a solution to the MEV problem that gives a near optimal result that can be solved in a reasonable amount of time. I layout the method and the formulas required for my solution. Additionally, I test my solution on synthesized data to show that it works as desired.

The question of finding the optimal size for battery energy storage systems (BESS) to be used for energy arbitrage and peak shaving has gained more and more interest in recent years. This is due to the increase in variability of electricity prices caused by the increase of renewable but also variable electricity production units in the electricity grid. The problem of finding the optimal size for a BESS is of high complexity. It includes many factors that affect the usefulness and the economic value of a BESS. This study includes a thorough literature study regarding different methods and techniques used for finding optimal size (both capacity and power) for a BESS. From the literature study two meta-heuristic algorithms were found to have been used with success for similar problems. The two algorithms were Genetic algorithm (GA) and Firefly algorithm (FF). These algorithms have in this thesis been tested in a case study optimizing the BESS capacity and power to either maximising the net present value (NPV) of investing in a Li-ion BESS of the LPF type or minimizing the levelized cost of storage (LCOS) for the BESS, with a project lifetime of 10 years. The BESS gains monetary value from energy arbitrage by being a middleman between a large residential house complex seen as the "user" with a predefined hourly electricity load demand and the electricity grid. For the case study a simplified charge and discharge dispatch schedule was implemented for the BESS with the focus of maximising the value of energy arbitrage. The case study was divided into 3 different cases, the base case where no instalment of a BESS was done. Case 2 included the instalment of the BESS whilst case 3 included installing both a BESS and an electrical heater (ELH). The electrical heater in case 3 was implemented to shift a heating load from the user to an electrical load, to save money as well as reduce CO2 emissions from a preinstalled gas heater used in the base case. The results showed that overall GA was a better optimization algorithm for the stated problem, having lower optimization time overall between 60%-70% compared to FF and depending on the case. For case 2, GA achieves the best LCOS with a value of 0.225 e/kWh, being 11.4% lower compared to using FF. Regarding NPV for case 2, FF achieves the best solutions at the lowest possible value in the search space for the capacity and power (i.e., 0.1 kWh for capacity and 0.1 kW for power), with an NPV at -51.5e, showing that for case 2 when optimizing for NPV an investment in a BESS is undesirable. GA finds better solutions for case 3 for both NPV and LCOS at 954,982e and 0.2305 e/kWh respectively, being 35.7% larger and 9.1% lower respectively compared to using FF. For case 3 it was shown that the savings from installing the ELH stands for a large portion of the profits, leading to a positive NPV compared to case 2 when it was not implemented. Finally, it was found that the GA can be a useful tool for finding optimal power and capacity for BESS instalments, compared to FF that got stuck at local optimums. However, it was seen that the charge and discharge dispatch schedule play an important role regarding the effectiveness of installing a BESS. As for some cases the BESS was only used 17% of all hours during a year (case 2, when optimizing for NPV). Therefore, further research is of interest into the schedule function and its role regarding finding the optimal BESS size. / Frågan angående hur man hittar den optimal storleken på en energilagringsenhet av batteritypen (BESS) som skall användas för energiarbitrage samt "peak shaving" har fått mer och mer uppmärksamhet de senaste åren. Detta sker på grund av en ökning av variabiliteten av elpriser, vilket i sig delvis kommer från ett ökat installerande av förnyelsebar, men då också variabla energiproduktionsenheter till elnätet. Problemet med att hitta den optimala storleken för en BESS är på grund av komplexitet i frågan. Det innehåller många faktorer som påverkar effektiviteten samt det ekonomiska värdet av en BESS. Denna avhandling innehåller en litteraturstudie om olika tekniker och metoder som används för att hitta den optimal lösningen för optimal storlek (kapacitet och kraft) på en BESS. Från litteraturstudien hittades två meta-heuristiska algoritmer som använts med succés på liknande problem. De två algoritmerna var "Genetic algorithm" (GA) och "Firefly algorithm (FF). Dessa algoritmer har i denna avhandling blivit testade i en fallstudie för att optimera kapacitet och kraft för en BESS genom att antingen maximera nettonuvärdet (NPV) som fås av att investera i en Li-ion BESS av typen LPF eller att minimera "levelized cost of storage" (LCOE) för en BESS med en livstid på 10 år. Detta genom att man får monetärt värde från att använda en BESS för energiarbitrage genom att vara en mellanhand mellan ett stort bostadskomplex som ses vara en "användare" med ett förbestämt elanvändningsmönster och elnätet. För fallstudien användes en simpel metodologi för laddnings- och urladdninsgschema för att maximera energiarbitrage. Fallstudien delades upp i tre olika fall, ett basfall där ingen installation av en BESS gjordes. I fall 2 installerades bara en BESS medans för fall 3 installerades både en BESS samt en elektrisk värmare (ELH) för att omvandla användarens termiska energianvändning till mer elektrisk energianvändning. Genom detta kan monetära besparingar göras samt reducera mängden CO2 utsläpp som annars hade kommit från en redan installerade gasvärmare, i basfallet.  Resultatet visade att totalt sätt var GA en bättre optimeringsalgoritm för det specifika problemet, med lägre optimeringstid på 60%-70% jämfört med FF och beroende på fall. För fall 2 hittar GA det lägsta värdet på LCOS på 0.225 e/kWh, och var då 11.4% lägre jämfört med FF. Angående NPV för fall 2 hittar FF den bästa lösningen på det minsta möjliga värdet på kraft och kapacitet i sökutrymmet (det vill säga 0.1 kWh för kapacitet och 0.1 kW för kraft), med ett NPV värde på -51.5e, vilket visar att för fall 2 när man optimerar för NPV så finns ingen ekonomisk vinning av att investera i en BESS. GA hittar den bästa lösningen för fall 3, både för NPV och LCOS på 954,982e och 0.2305 e/kWh respektivt, vilket är 35.7% större och 9.1% lägre respektivt jämfört när man använder FF. För fall 3 visade resultaten att besparingarna från att installera en ELH stod för den större delen av alla vinster, vilket ledde till positiva värden för NPV. Slutligen visade resultaten att GA kan vara ett användbart verktyg för att hitta den optimala lösningen för storleken på en BESS, jämfört med FF som fastande på lokal optimala lösningar. Dock kunde resultaten också visa att laddnings- och urladdninsgschemat använt i fallstudien spelade en viktig roll angående effektiviteten med att installera en BESS. I vissa fall så användes BESS:en så lite som 17% av alla timmar på ett år (fall 2, optimering av NPV). Därför är det ett stort intresse att göra fortsatt forskning på andra laddnings- och urladdninsgscheman och dess roll med att hitta en optimal storlek på en BESS.

This dissertation consists of three essays. The first essay focuses on idiosyncratic volatility as a primary arbitrage cost for short sellers. Previous studies document (i) negative abnormal returns for high relative short interest (RSI) stocks, and (ii) positive abnormal returns for low RSI stocks. We examine whether these market inefficiencies can be explained by arbitrage limitations, especially firms' idiosyncratic risk. Consistent with limits to arbitrage hypothesis, we document an abnormal return of -1.74% per month for high RSI stocks (>=95th percentile) with high idiosyncratic volatility. However, for similar level of high RSI, abnormal returns are economically and statistically insignificant for stocks with low idiosyncratic volatility. For stocks with low RSI, the returns are positively related to idiosyncratic volatility. These results imply that idiosyncratic risk is a potential reason for the inability of arbitrageurs to extract returns from high and low RSI portfolios. The second essay investigates market efficiency in the absence of limits to arbitrage on short selling. Theoretical predictions and empirical results are ambiguous about the effect of short sale constraints on security prices. Since these constraints cannot be eliminated in equity markets, we use trades from futures markets where there is no distinction between short and long positions. With no external constraints on short positions, we document a weekend effect in futures markets which is a result of asymmetric risk between long and short positions around weekends. The premium is higher in periods of high volatility when short sellers are unwilling to accept higher levels of risk. On the other hand, riskiness of long positions does not seem to have a similar impact on prices. The third essay studies investor behaviors that generate mispricing by examining relationship between stock price and future returns. Based on traditional finance theory, valuation should not depend on nominal stock prices. However, recent literature documents that preference of retail investors for low price stocks results in their overvaluation. Motivated by this preference, we re-examine the relationship between stock price and expected return for the entire U.S. stock market. We find that stock price and expected returns are positively related if price is not confounded with size. Results in this paper show that, controlled for size, high price stocks significantly outperform low price stocks by an abnormal 0.40% per month. This return premium is attributed to individual investors' preference for low price stocks. Consistent with costly arbitrage, the return differential between high and low price stocks is highest for the stocks which are difficulty to arbitrage. The results are robust to price cut-off of $5, and in different sub-periods. / Ph. D.

Investing in the stock market offers opportunities for wealth accumulation through variousstrategies. This thesis explores the pairs trading strategy with dual-class stocks differingonly in voting rights, aiming to reduce portfolio risk and outperform the market bench-mark. Using data from the Swedish Large Cap index (2003-2023), the study benchmarksthe strategy’s performance against the OMXSPI index, assessing total return, CAGR andthe Sharpe ratio for three different strategies. Depending on the predefined thresholds ofthe trading strategy, the study concludes that pairs trading can surpass a buy-and-holdapproach, showing the effectiveness of a market neutral trading strategy.

"Mémoire présenté à la Faculté des Études supérieures En vue de l'obtention du grade de Maîtrise en droit (LL.M.) option : Droit des affaires". Ce mémoire a été accepté à l'unanimité et classé parmi les 15% des mémoires de la discipline. / L'arbitrage étant une institution basée sur la volonté des parties, le consentement à la procédure arbitrale multipartite soulève de nombreuses questions relativement à la manière dont les parties expriment leur intention de faire partie d'une instance unique. Cette étude vise à déterminer les conditions dans lesquelles l'arbitre peut arriver à unifier la résolution des litiges qui impliquent les groupements de sociétés. Le plus naturel des moyens pour aboutir à une procédure multipartite est de prévoir cette possibilité à travers la convention d'arbitrage. Cela peut notamment provenir de la signature d'une convention d'arbitrage unique par toutes les parties concernées. Dans certains cas précis, l'arbitrage multipartite peut également résulter de plusieurs conventions d'arbitrage spécialement lorsque les parties participent à la réalisation d'un même ouvrage. Cependant, il arrive souvent qu'une partie qui n'a pas signé la convention d'arbitrage soit obligée à participer à l'instance. Même sans y être obligée, une partie non-signataire de la convention d'arbitrage peut aussi demander de participer à l'arbitrage pour défendre ses intérêts. Pour pouvoir admettre la participation à la procédure d'un tiers non-signataire de la convention d'arbitrage, les arbitres ont recours à plusieurs notions prévues par les droits internes. C'est ainsi que la levée du voile corporatif, la théorie de la réalité économique et le principe de l'estoppel constituent les meilleurs outils pour les arbitres d'amener à la procédure, par force ou sur demande, un non-signataire de la convention d'arbitrage. Enfin, les mécanismes du Code civil servent efficacement à neutraliser les effets du principe de relativité de la convention d'arbitrage. Il s'agit notamment de la bonne foi, du mandat, de la stipulation pour autrui et de la cession. / Arbitration as an institution based on the intention of the parties, the consent on the multi-party arbitration procedure raises many problems relating to the way in which the parties express their intention to participate in a unique arbitration forum. This study aims to determinate the manner in which the arbitrator can join disputes resolution involving the groups of companies. The normal way to get a multi-party procedure is to provide it in an arbitration clause. This can be by signing a single arbitration agreement by all the parties involved. In certain cases, the multi-party arbitration can also be possible with several arbitration agreements especially when the parties took part in carrying out ofthe same economic operation. However, in other situations, the multi-party arbitration procedure is unrelated to consent. A non-signatory party can nevertheless be bound by an arbitration agreement signed by an other party. To allow the participation in the arbitration procedure of a third party non-signatory of the arbitration agreement, the arbitrators use several concepts provided chiefly by the national laws. 80, the lifting of the corporate veil, the doctrine of economic reality and estoppel, are the best tools for the arbitrators to bring to the arbitration procedure, by force or on request, a non-signatory of the arbitration agreement. Lastly, the mechanisms of the Civil code are used with efficiency by arbitrators to neutralize the effects of the relativity principle of the arbitration agreement. Those mechanisms are in particular the good faith, mandate, stipulation for another and assignment.

Ce mémoire jette un regard critique sur une question aussi intéressante qu’actuelle à savoir, quelles sont les règles juridiques applicables aux traités d’investissement en cas de succession d’États. La gestion du contentieux relatif aux investissements internationaux révèle une Convention de 1978 inadaptée, des décisions jurisprudentielles qui pataugent et une doctrine qui s’interroge. Le présent mémoire qui aborde l’interface entre le droit international général et le droit international de l’investissement a permis de savoir que c’est un ensemble de règles, mettant en bonne place la Convention de 1969 comme adjuvant à celle de 1978, qui régit la problématique fondamentale qui est en fait le sort du consentement à l’arbitrage exprimé dans les traités de l’État prédécesseur. L’intention explicite ou implicite des parties, la qualification des traités d’investissement à l’aune de la distinction entre traités réels et traités personnels sont autant de pistes explorées pour répondre à la question fondamentale et accessoirement à celle de la responsabilité internationale de l’État sur le fondement des traités d’investissement lorsqu’on aborde la question de la clause de survie. / This study examines critically an interesting and timely issue, namely, the identification of the legal rules applicable to investment treaties in the event of State succession. The application of the Convention of 1978 has proven to be unsuitable, the jurisprudence uncertain and the doctrine hesitating. This paper draws resources from both general international law and international law of investment to argue that only a connection between the Convention of 1969 and the Convention of 1978 can govern satisfactorily the fate of the consent for arbitration from the predecessor State. The study highlights the explicit or implicit intention of the parties and the distinction between real and personal treaties in order to substantiate the solution provided to the main question. Incidentally it makes considerations on the international responsibility of the State when addressing the issue of the survival clause of investment treaties.