This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.

This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.

Stochastic price models have proven material to decision making in the oil industry when accurate valuations are important, but little consideration is given to their impact on decisions based on relative project rankings. Traditional industry economic analysis methods do not usually consider uncertainty in oil price, although the real options literature has shown that this practice underestimates the value of projects that have flexibility. Monetary budget constraints are not always the limiting constraints in decision making; there may be other constraints that limit the number of projects a company can undertake. We consider building a portfolio of upstream petroleum development projects to determine the relevance of stochastic price models to a decision for which accurate valuations may not be important. The results provide guidelines to determine when a stochastic price model should be used in economic analysis of petroleum projects. / text

This study investigates the cryptocurrency called bitcoin. A cryptocurrency is a type of currency that depends on cryptography to issue new units instead of depending on government decree like fiat currencies. The study will first explain some of the technical details that make bitcoin work. This is necessary to lay groundwork to get to the actual aim of the study, namely investigating the economic aspects of bitcoin. The study will evaluate bitcoin, and other cryptocurrencies, along with fiat currencies against certain definitions. In the process it will introduce a new subclass of cryptocurrency - the sovereign cryptocurrency. Bitcoin’s implied monetary policy will also be discussed, as well as the problems it creates for central banks. A hypothesis on the behaviour of the bitcoin price will be explained and research will be provided to support the acceptance of the hypothesis. Using this hypothesis, a stochastic pricing model for bitcoin will be derived. Arbitrage trading strategies will also be provided that explain certain price constraints that operate in the bitcoin market. The dissertation will also introduce a means to improve the anonymity of a user of bitcoin and will reason that improvements such as these and others will increase the use of bitcoin. Therefore, improvements to anonymity will increase the economic relevance of bitcoin and increase its competitive edge over the traditional banking system. It will be reasoned, based on the possible problems created by bitcoin’s monetary policy, as well as the growth projections implied by the stochastic pricing model, and the increased economic relevance due to improvements in anonymity, that central banks would need to create their own cryptocurrency that conforms to certain requirements – the previously introduced sovereign cryptocurrency. The study will conclude by explaining the technical changes needed for a fork of bitcoin to become a sovereign cryptocurrency, as well as a mathematical model to control the monetary policy of the sovereign cryptocurrency. As its aim, adaptive monetary policy will have stable prices for the economy using the sovereign cryptocurrency to price its goods and services. Please note, that while every effort was made to use published references, the field of cryptocurrencies is very young and changing constantly. Thus, most publications on the subject are simply placed on websites on the internet. This is especially true for the work relating to the founding of the field, and the data sources of the operation of the cryptocurrencies. Therefore a lot of the references do refer to websites on the internet. / Dissertation (MSc)--University of Pretoria, 2019. / Mathematics and Applied Mathematics / MSc / Unrestricted

Through integrated modeling of power system operations and market risks, this thesis addresses a variety of important issues on market signals modeling, generation capacity scheduling, and electricity forward trading. The first part of the thesis addresses a central problem of transmission investment which is to model market signals for transmission adequacy. The proposed system simulation framework, combined with the stochastic price model, provides a powerful tool for capturing the characteristics of market prices dynamics and evaluating transmission investment. We advocate the use of an AC power flow formulations instead since it allocates transmission losses correctly and reveals the economic incentives of voltage requirements. By incorporating reliability constraints in the market dispatch, the resulting market prices yield incentives for market participants to invest in additional transmission capacity. The second part of the thesis presents a co-optimization modeling framework that incorporates market participation and market price uncertainties into the capacity allocation decision-making problem through a stochastic programming formulation. Optimal scenario-dependent generation scheduling strategies are obtained. The third part of the thesis is devoted to analyzing the risk premium present in the electricity day-ahead forward price over the real-time spot price. This study establishes a quantitative model for incorporating transmission congestion into the analysis of electricity day-ahead forward risk premium. Evidences from empirical studies confirm the significant statistical relationship between the day-ahead forward risk premium and the shadow price premiums on transmission flowgates.