On The Validity of The Geometric Brownian Motion Assumption

Marathe, Rahul R.; Ryan, Sarah M.

doi:10.1080/00137910590949904

Cited by 115 publications

(73 citation statements)

References 14 publications

(16 reference statements)

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“…The assumption of exponentially increasing demand over an infinite horizon is strong. However, the geometric Brownian motion assumption for demand is supported by statistical analysis of the actual usage of electric power and airline travel over recent decades [18]. Also, the expansion size policy assumed by Whitt [32] for geometric Brownian motion demand without lead times and with no particular assumption about expansion costs, which is the same policy used in this paper, was found to match the actual industry-wide expansions of chemical production capacity over two decades [13].…”

Section: Problem Definition and Notationmentioning

confidence: 89%

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

Pak

Pornsalnuwat

Ryan

2004

The Engineering Economist

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We formulate a model of capacity expansion that is relevant to a service provider for whom the cost of capacity shortages would be considerable but difficult to quantify exactly. Due to demand uncertainty and a lead time for adding capacity, not all shortages are avoidable. In addition, technological innovations will reduce the cost of adding capacity but may not be completely predictable. Analytical expressions for the infinite horizon expansion cost and shortages are optimized numerically. Sensitivity analyses allow us to determine the impact of technological change on the optimal timing and sizes of capacity expansions to account for economies of scale, the time value of money and penalties for insufficient capacity. The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand with Lead Times AbstractWe formulate a model of capacity expansion that is relevant to a service provider for whom the cost of capacity shortages would be considerable but difficult to quantify exactly. Due to demand uncertainty and a lead time for adding capacity, not all shortages are avoidable. In addition, technological innovations will reduce the cost of adding capacity but may not be completely predictable. Analytical expressions for the infinite horizon expansion cost and shortages are optimized numerically. Sensitivity analyses allow us to determine the impact of technological change on the optimal timing and sizes of capacity expansions to account for economies of scale, the time value of money and penalties for insufficient capacity.

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Section: Problem Definition and Notationmentioning

confidence: 89%

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

Pak

Pornsalnuwat

Ryan

2004

The Engineering Economist

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“…The uncertainty in demand growth in each region is modeled by a Geometric Brownian Motion (GBM) (Marathe and Ryan, 2005). The model takes into consideration the cross-correlation between the growth rates of both systems.…”

Section: < Figure 1 Around Here >mentioning

confidence: 99%

Designing regulatory frameworks for merchant transmission investments by real options analysis

Pringles¹,

Olsina²,

Garcés³

2014

Energy Policy

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In deregulated electricity markets, the transmission network is a key infrastructure for enabling competition in the generation sector. A deficient expansion of the transmission grid prevents the realization of the benefits in terms of efficiency associated with market mechanisms. Consequently, it is essential to provide clear investment policies and economic signals to attract timely and efficient transmission investments in order to develop the system at minimum cost meeting the requirements of generators and consumers, while keeping adequate levels of service quality and reliability. This paper proposes a modern tool of economic evaluation based on Real Options Analysis that provides the regulator the ability to assess various incentives that would lead transmission investors to make efficient decisions in highly uncertain environments. Real Options properly values partially irreversible investment decisions, such as to defer, modify or abandon an investment project in response to the arrival of new information or as uncertainties are resolved. Decisions are evaluated from the point of view of a transmission investor trying to maximize its own profits in the time period set to recover the capital invested. The results allow the study of the behavior of transmission investors regarding their decision making when they have the possibility to manage the option to defer, under different regulatory schemes that encourage the expansion of the transmission system.

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“…Nesse caso, é necessário removê-la para que a aceitação ou rejeição de um processo estocástico como um MGB não seja equivocada (Marathe & Ryan, 2005).…”

Section: Processo De Wiener E Movimento Geométrico Brownianounclassified

“…Conforme indicado por Marathe & Ryan (2005), para testar se o MGB é válido para representar o crescimento da demanda, é necessário dessazonalizar os dados. Para tanto, com base na metodologia descrita na seção 3.3.2 (Séries com sazonalidade), foram dessazonalizados os dados utilizando as equações (3.23), (3.24) e (3.25).…”

Section: Variáveis De Incerteza E Definição Dos Parâmetros Dos Procesunclassified

Decisão De Investimento Em Projetos De Serviços Pós-Venda

CESAR¹

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A Deus, por toda a proteção e por iluminar e abençoar minha vida.Ao meu esposo e meu melhor amigo, Igor, por todo amor, carinho, paciência e dedicação.Aos meus pais, Moasir e Joçania, pelo amor, pela educação, pelos valores e por sempre me oferecerem seu colo e seu apoio me dando a certeza de se manterem, mesmo à distância, meu porto seguro.À minha irmã, Cecília, pelo amor, pela alegria, pela admiração e pelo incentivo a ser sempre um exemplo.Aos meus sogros, Ademir e Neuza, pelo amor e cuidado de pais quando os meus estavam tão distantes. Por todo o carinho e por todo o suporte.À minha querida orientadora, Professora Frances Fischberg Blank, por acreditar e me apoiar durante todas as etapas da dissertação. Por todos os ensinamentos, contribuições, tempo e pela enorme dedicação.A todos os professores e funcionários do Departamento de Engenharia Industrial da PUC-Rio, pela dedicação e atenção, especialmente ao Orivalde e ao Eduardo.Aos meus amigos e colegas de mestrado e de trabalho (Felipe, Simone, Michael, Fernando, Kathy, Tom), pela companhia, pelo apoio e pela amizade. Palavras-ChaveServiços pós-venda; custos logísticos e tributários; análise de viabilidade; opções reais; opção perpétua. Prior to taking investment decision in after-sales services projects, the logistics costs of its operations must be known and considered, they may include transportation costs, originated from routing, and logistics and import tax related

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On The Validity of The Geometric Brownian Motion Assumption

Cited by 115 publications

References 14 publications

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

Designing regulatory frameworks for merchant transmission investments by real options analysis

Decisão De Investimento Em Projetos De Serviços Pós-Venda

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