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1 
Merton JumpDiffusion Modeling of Stock Price DataTang, Furui January 2018 (has links)
In this thesis, we investigate two stock price models, the BlackScholes (BS) model and the Merton JumpDiffusion (MJD) model. Comparing the logarithmic return of the BS model and the MJD model with empirical stock price data, we conclude that the Merton JumpDiffusion Model is substantially more suitable for the stock market. This is concluded visually not only by comparing the density functions but also by analyzing mean, variance, skewness and kurtosis of the logreturns. One technical contribution to the thesis is a suggested decision rule for initial guess of a maximum likelihood estimation of the MJDmodeled parameters.

2 
Performance modelling of wormholerouted hypercubes with bursty traffice and finite buffersKouvatsos, Demetres D., Assi, Salam, OuldKhaoua, M. January 2005 (has links)
An open queueing network model (QNM) is proposed for wormholerouted hypercubes with finite
buffers and deterministic routing subject to a compound Poisson arrival process (CPP) with geometrically
distributed batches or, equivalently, a generalised exponential (GE) interarrival time distribution. The GE/G/1/K
queue and appropriate GEtype flow formulae are adopted, as costeffective building blocks, in a queuebyqueue
decomposition of the entire network. Consequently, analytic expressions for the channel holding time, buffering
delay, contention blocking and mean message latency are determined. The validity of the analytic approximations
is demonstrated against results obtained through simulation experiments. Moreover, it is shown that the wormholerouted
hypercubes suffer progressive performance degradation with increasing traffic variability (burstiness).

3 
Hedging no modelo com processo de Poisson composto / Hedging in compound Poisson process modelSung, Victor Sae Hon 07 December 2015 (has links)
Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de meanvariance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy purejump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using meanvariance hedging and dynamic programming.

4 
Mathematical Modeling and Analysis of Options with JumpDiffusion VolatilityAndreevska, Irena 09 April 2008 (has links)
Several existing pricing models of financial derivatives as well as the effects of volatility risk are analyzed. A new option pricing model is proposed which assumes that stock price follows a diffusion process with squareroot stochastic volatility. The volatility itself is meanreverting and driven by both diffusion and compound Poisson process. These assumptions better reflect the randomness and the jumps that are readily apparent when the historical volatility data of any risky asset is graphed. The European option price is modeled by a homogeneous linear secondorder partial differential equation with variable coefficients. The case of underlying assets that pay continuous dividends is considered and implemented in the model, which gives the capability of extending the results to American options. An American option price model is derived and given by a nonhomogeneous linear second order partial integrodifferential equation. Using Fourier and Laplace transforms an exact closedform solution for the price formula for European call/put options is obtained.

5 
Hedging no modelo com processo de Poisson composto / Hedging in compound Poisson process modelVictor Sae Hon Sung 07 December 2015 (has links)
Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de meanvariance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy purejump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using meanvariance hedging and dynamic programming.

6 
Hedging no modelo com processo de Poisson composto / Hedging in compound Poisson process modelSae Hon Sung, Victor 07 December 2015 (has links)
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Previous issue date: 20151207 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy purejump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using meanvariance hedging and dynamic programming. / Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de meanvariance hedging e princípio da programação dinâmica.

7 
Performance Analysis of Virtualisation in a Cloud Computing Platform. An application driven investigation into modelling and analysis of performance vs security tradeoffs for virtualisation in OpenStack infrastructure as a service (IaaS) cloud computing platform architectures.Maiyama, Kabiru M. January 2019 (has links)
Virtualisation is one of the underlying technologies that led to the success of cloud computing platforms (CCPs). The technology, along with other features such as multitenancy allows delivering of computing resources in the form of service through efficient sharing of physical resources. As these resources are provided through virtualisation, a robust agreement is outlined for both the quantity and qualityofservice (QoS) in a service level agreement (SLA) documents. QoS is one of the essential components of SLA, where performance is one of its primary aspects. As the technology is progressively maturing and receiving massive acceptance, researchers from industry and academia continue to carry out novel theoretical and practical studies of various essential aspects of CCPs with significant levels of success.
This thesis starts with the assessment of the current level of knowledge in the literature of cloud computing in general and CCPs in particular. In this context, a substantive literature review was carried out focusing on performance modelling, testing, analysis and evaluation of Infrastructure as a Service (IaaS), methodologies.
To this end, a systematic mapping study (SMSs) of the literature was conducted. SMS guided the choice and direction of this research.
The SMS was followed by the development of a novel open queueing network model (QNM) at equilibrium for the performance modelling and analysis of an OpenStack IaaS CCP. Moreover, it was assumed that an external arrival pattern is Poisson while the queueing stations provided exponentially distributed service times. Based on Jackson’s theorem, the model was exactly decomposed into individual M/M/c (c ≥ 1) stations. Each of these queueing stations was analysed in isolation, and closedform expressions for key performance metrics, such as mean response time, throughput, server (resource) utilisation as well as bottleneck device were determined.
Moreover, the research was extended with a proposed open QNM with a bursty external arrival pattern represented by a Compound Poisson Process (CPP) with geometrically distributed batches, or equivalently, variable Generalised Exponential (GE) interarrival and service times. Each queueing station had c (c ≥ 1) GEtype servers. Based on a generic maximum entropy (ME) product form approximation, the proposed open GEtype QNM was decomposed into individual GE/GE/c queueing stations with GEtype interarrival and service times. The evaluation of the performance metrics and bottleneck analysis of the QNM were determined, which provided vital insights for the capacity planning of existing CCP architectures as well as the design and development of new ones. The results also revealed, due to a significant impact on the burstiness of interarrival and service time processes, resulted in worstcase performance bounds scenarios, as appropriate.
Finally, an investigation was carried out into modelling and analysis of performance and security tradeoffs for a CCP architecture, based on a proposed generalised stochastic Petri net (GSPN) model with securitydetection control model (SDCM). In this context, ‘optimal’ combined performance and security metrics were defined with both Mtype or GEtype arrival and service times and the impact of security incidents on performance was assessed. Typical numerical experiments on the GSPN model were conducted and implemented using the Möbius package, and an ‘optimal’ tradeoffs were determined between performance and security, which are crucial in the SLA of the cloud computing services. / Petroleum technology development fund (PTDF) of the government of Nigeria
Usmanu Danfodiyo University, Sokoto

8 
Entropy Maximisation and Open Queueing Networks with Priority and Blocking.Kouvatsos, Demetres D., Awan, Irfan U. January 2003 (has links)
No / A review is carried out on the characterisation and algorithmic implementation of an extended productform approximation, based on the principle of maximum entropy (ME), for a wide class of arbitrary finite capacity open queueing network models (QNMs) with service and space priorities. A single server finite capacity GE/GE/1/N queue with R (R>1) distinct priority classes, compound Poisson arrival processes (CPPs) with geometrically distributed batches and generalised exponential (GE) service times is analysed via entropy maximisation, subject to suitable GEtype queueing theoretic constraints, under preemptive resume (PR) and headofline (HOL) scheduling rules combined with complete buffer sharing (CBS) and partial buffer sharing (PBS) management schemes stipulating a sequence of buffer thresholds {N=(N1,¿,NR),0<Ni¿Ni¿1,i=2,¿,R}. The GE/GE/1/N queue is utilised, in conjunction with GEtype first two moment flow approximation formulae, as a costeffective building block towards the establishment of a generic ME queuebyqueue decomposition algorithm for arbitrary open QNMs with space and service priorities under repetitive service blocking with random destination (RSRD). Typical numerical results are included to illustrate the credibility of the ME algorithm against simulation for various network topologies and define experimentally pessimistic GEtype performance bounds. Remarks on the extensions of the ME algorithm to other types of blocking mechanisms, such as repetitive service blocking with fixed destination (RSFD) and blockingafterservice (BAS), are included.

9 
Highway Development DecisionMaking Under Uncertainty: Analysis, Critique and AdvancementElKhatib, Mayar January 2010 (has links)
While decisionmaking under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous.
In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model.
This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decisionmaking. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavytailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives.
Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decisionmaking process. This furthers the quest for optimality in highway projects and beyond.

10 
Highway Development DecisionMaking Under Uncertainty: Analysis, Critique and AdvancementElKhatib, Mayar January 2010 (has links)
While decisionmaking under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous.
In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model.
This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decisionmaking. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavytailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives.
Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decisionmaking process. This furthers the quest for optimality in highway projects and beyond.

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