1,720,984 research outputs found
Three Way Duels: Infinite Games on the Unit Square
No full textWith the growing wealth and economy of a country, there are an increasing amount of small and big businesses. Every company has its own marketing strategy that it uses in order to lure customers away from their competition and increase their sales. Choosing the perfect time to advertise or discount several products is of essence for a company to gain more money than their competition. These type of marketing games are all slight variations of duels. The purpose of this report is to research how this duel is played most optimal when there are two or more participants. Several types of two-player duels shall be analysed first in order to understand and analyse a three-player duel.Applied Mathematic
Riemann's Explicit Formula and the Prime Number Theorem
No full textThis thesis presents an insight in the Riemann zeta function and the prime number theorem at an undergraduate mathematical level. The main goal is to construct an explicit formula for the prime counting function and to prove the prime number theorem using the zeta function and a Tauberian theorem. The Riemann zeta function can be continued analytically to the whole complex plane except at s = 1. Two proofs of this continuation were given by Bernhard Riemann in his famous article ``Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse'' from 1859. Those proofs are studied in detail in this thesis after introducing all the required foreknowledge on the gamma function. The prime counting function π(x) counts the number of primes less than or equal to x. An explicit formula for π(x) in terms of the nontrivial zeros of the zeta function will be constructed in a similar way as Riemann did in his article. Finally, the prime number theorem will be proved. This theorem describes the asymptotic distribution of the primes among the natural numbers. Using the analytic continuation of the zeta function and a Tauberian theorem, the prime number theorem can be proved quite easily with only basic theory from complex analysis.Applied Mathematic
Distributing tasks in committees: An algorithmic research in a cooperative game theory problem
No full textCooperative game theory studies multi-agent environments where agents are able to make binding agreements. A lot has been written about dividing goods or other positive gains among the agents. This study investigates ways to distribute tasks with a negative utility in a strategyproof way. The intended application is a group of people or companies who can distribute such tasks between them to benefit from each other. The agents value tasks being done, but would rather not do it themselves. They can however, distribute the tasks to mutually benefit. Agents value tasks differently and also have different costs for them. This study investigates the theoretical properties of this problem. Particularly, we look at the Core, which is the set of solutions where agents have no incentive to form coalitions between them and ignore the result of the mechanism. Then, two algorithms are proposed to solve the problem. Finally, experiments are done to predict what results would occur in practice.Computer Scienc
Cumulative Prospect Theory in Option Valuation and Portfolio Management
No full textThis thesis deals with different models for decision-making under risk in financial applications, mainly models that incorporate irrational human behavior. First of all, traditional expected utility theory is considered. Hereafter, two models that incorporate irrational human behavior are discussed and compared: prospect theory and cumulative prospect theory. Next, these models are applied to option pricing. The influence of various levels of sentiment on the option price is investigated and the prices are compared with Black-Scholes prices. Also, a sensitivity analysis is done in order to investigate the influence of the prospect parameters on the option price. Furthermore, the different models discussed are applied to portfolio management for which the optimal wealth profiles are analyzed and compared. Moreover, a data analysis with a portfolio of stocks of different indices is done in which it is investigated whether the parameter estimates used for prospect sentiment are applicable to financial data. Finally, a hedge test under prospect sentiment is performed in order to investigate whether a delta-hedge leads to sufficient results in case of asset price paths under prospect sentiment
Oplossingen voor Dreshers hoger lager spel voor N <= 980
No full textMelvin Dresher beschouwde in zijn boek uit 1961 over speltheorie een getallenraadspel over N getallen. Hij liet zien hoe de optimale strategieën van beide spelers kon worden gevonden met behulp van lineair programmeren. Later toonde Selmer Johnson oplossingen voor N<=11 en merkte op dat de berekeningen steeds complexer werden bij toenemende N. Deze thesis beschrijft technieken om het spel op te lossen voor N<=980. Het algoritme van Dresher vormt nog steeds de basis, maar er zijn enkele aanpassingen. Niet alle voorwaarden worden bijvoorbeeld in het begin gegenereerd. Voorwaarden worden alleen op het moment dat ze nodig zijn gevonden met een subroutine. Dit is een vorm van delayed column generation. Er wordt ook gebruik gemaakt van heuristieken, zoals het schatten van de optimale kansverdeling van één van de spelers. Dit werk verschaft meer inzicht in het patroon van de oplossingen van dit spel en of enkele eerder geformuleerde vermoedens van Selmer Johnson en Edgar Gilbert over dit spel kloppen
Modelling Terrorist Attacks
No full textThis thesis adds to quantitative literature on terrorism by examining the relationship between various annual country statistics and the number of terrorist attacks. In addition, it assesses the potential of forecasting terrorism. Combining an extensive review of literature from social science, with data analysis of the Global Terrorism Database, results in a specific selection of attacks on country-level, along with various factors that allegedly affect terrorism. It is shown that, under certain conditions, the countries can be fit by a nonhomogeneous Poisson process model with a Weibull baseline intensity and a piecewise constant covariates component. For three out of five countries, the in-sample results are satisfactory, providing a tentative answer to the general debate whether terrorism can be explained by root causes. Out-of-sample results for Afghanistan and Somalia are promising for future research and implementation in policy making.Applied Mathematic
Using futures in yield curve calibration
No full textThe yield curve represents market supply and demand implied expectations of future interest rates and is calibrated from the most liquidly traded interest rate derivatives like cash deposits, forward rate agreeents, swaps and futures. Due to the daily margining mechanism of futures contracts, interest rate futures require the substraction of a convexity adjustment in order for them to be used in curve calibration. It is common practice to use externally computed convexity adjustments, which treats the convexity adjustment as a black-box parameter. We will argue the inherent relationship between the convexity adjustment and cap/floor volatility smiles and derive a nested calibration algorithm for the simultaneous calibration of the yield curve to futures and the convexity adjustment to cap/floor volatility surfaces. This introduces dependencies of the yield curve to option volatilities and we will argue that for simple interest rate derivatives the implied vegas are negligible.
Akiyama's Nim
No full textAkiyama’s Nim is een 3d versie van een onpartijdig combinatorisch spel genaamd Wythoffs Nim. Het spel van Wythoff kan met twee stapels munten gespeeld worden. Elke positie in dit spel komt overeen met een getal dat als temperatuur te zien is waarbij posities met temperatuur 0 koud genoemd worden. Er is een makkelijke formule voor de koude posities van Wythoffs spel. Voor hogere temperaturen zijn geen gesloten formules bekend. Door het aantal toegestane zetten te beperken is wel een formule voor posities met hogere temperaturen te vinden. De formule voor posities met temperatuur 1 en 2 worden voor deze beperkte versie gegeven. Nu kan het spel van Akiyama bekeken worden, dit is een versie van Wythoff met 3 stapels munten. Van dit spel is geen formule voor de koude posities bekend. Het is al heel moeilijk om een correct algoritme te maken. Daarom bekijk ik in dit verslag een vereenvoudigd algoritme. Van dit algoritme kunnen de onder- en bovengrenzen worden berekend die een indicatie geven van de afstand tussen koude posities. Het vermoeden is dat deze koude posities op een lijn liggen en er wordt een vermoeden van de helling van deze lijn gegeven
An analytical approach to the Generalized Tally Game
No full textIn this thesis, we find optimal strategies for both players in the generalized tally game, mainly using Glicksberg's theorem and minimax theorem. Analytical and numerical solutions provided for the tally game with one draws and with two draws.Applied Mathematic
The Pell Tower and Ostronometry
Full text linkConway and Ryba considered a table of bi-infinite Fibonacci sequences and
discovered new interesting patterns. We extend their considerations to tables
that are defined by the recurrence for natural numbers
. In our search for new patterns we run into a Red Wall and exotic
numeration systems
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