The knapsack problem approach in solving partial hedging problems of options

En option är ett finansiellt kontrakt som ger dess innehavare en rättighet (men medför ingen skyldighet) att sälja eller köpa någonting (till exempel en aktie) till eller från säljaren av optionen till ett visst pris vid en bestämd tidpunkt i framtiden. Den som säljer optionen binder sig till att gå med på denna framtida transaktion ifall optionsinnehavaren längre fram bestämmer sig för att inlösa optionen. Säljaren av optionen åtar sig alltså en risk av att den framtida transaktion som optionsinnehavaren kan tvinga honom att göra visar sig vara ofördelaktig för honom. Frågan om hur säljaren kan skydda sig mot denna risk leder till intressanta optimeringsproblem, där målet är att hitta en optimal skyddsstrategi under vissa givna villkor. Sådana optimeringsproblem har studerats mycket inom finansiell matematik. Avhandlingen "The knapsack problem approach in solving partial hedging problems of options" inför en ytterligare synpunkt till denna diskussion: I en relativt enkel (ändlig och komplett) marknadsmodell kan nämligen vissa partiella skyddsproblem beskrivas som så kallade kappsäcksproblem. De sistnämnda är välkända inom en gren av matematik som heter operationsanalys. I avhandlingen visas hur skyddsproblem som tidigare lösts på andra sätt kan alternativt lösas med hjälp av metoder som utvecklats för kappsäcksproblem. Förfarandet tillämpas även på helt nya skyddsproblem i samband med så kallade amerikanska optioner.

Production of Mg(OH)2 from Mg-silicate rock for CO2 mineral sequestration

Sequestration of carbon dioxide in mineral rocks, also known as CO2 Capture and Mineralization (CCM), is considered to have a huge potential in stabilizing anthropogenic CO2 emissions. One of the CCM routes is the ex situ indirect gas/sold carbonation of reactive materials, such as Mg(OH)2, produced from abundantly available Mg-silicate rocks. The gas/solid carbonation method is intensively researched at Åbo Akademi University (ÅAU ), Finland because it is energetically attractive and utilizes the exothermic chemistry of Mg(OH)2 carbonation. In this thesis, a method for producing Mg(OH)2 from Mg-silicate rocks for CCM was investigated, and the process efficiency, energy and environmental impact assessed. The Mg(OH)2 process studied here was first proposed in 2008 in a Master’s Thesis by the author. At that time the process was applied to only one Mg-silicate rock (Finnish serpentinite from the Hitura nickel mine site of Finn Nickel) and the optimum process conversions, energy and environmental performance were not known. Producing Mg(OH)2 from Mg-silicate rocks involves a two-staged process of Mg extraction and Mg(OH)2 precipitation. The first stage extracts Mg and other cations by reacting pulverized serpentinite or olivine rocks with ammonium sulfate (AS) salt at 400 - 550 oC (preferably < 450 oC). In the second stage, ammonia solution reacts with the cations (extracted from the first stage after they are leached in water) to form mainly FeOOH, high purity Mg(OH)2 and aqueous (dissolved) AS. The Mg(OH)2 process described here is closed loop in nature; gaseous ammonia and water vapour are produced from the extraction stage, recovered and used as reagent for the precipitation stage. The AS reagent is thereafter recovered after the precipitation stage. The Mg extraction stage, being the conversion-determining and the most energy-intensive step of the entire CCM process chain, received a prominent attention in this study. The extraction behavior and reactivity of different rocks types (serpentinite and olivine rocks) from different locations worldwide (Australia, Finland, Lithuania, Norway and Portugal) was tested. Also, parametric evaluation was carried out to determine the optimal reaction temperature, time and chemical reagent (AS). Effects of reactor types and configuration, mixing and scale-up possibilities were also studied. The Mg(OH)2 produced can be used to convert CO2 to thermodynamically stable and environmentally benign magnesium carbonate. Therefore, the process energy and life cycle environmental performance of the ÅAU CCM technique that first produces Mg(OH)2 and the carbonates in a pressurized fluidized bed (FB) were assessed. The life cycle energy and environmental assessment approach applied in this thesis is motivated by the fact that the CCM technology should in itself offer a solution to what is both an energy and environmental problem. Results obtained in this study show that different Mg-silicate rocks react differently; olivine rocks being far less reactive than serpentinite rocks. In summary, the reactivity of Mg-silicate rocks is a function of both the chemical and physical properties of rocks. Reaction temperature and time remain important parameters to consider in process design and operation. Heat transfer properties of the reactor determine the temperature at which maximum Mg extraction is obtained. Also, an increase in reaction temperature leads to an increase in the extent of extraction, reaching a maximum yield at different temperatures depending on the reaction time. Process energy requirement for producing Mg(OH)2 from a hypothetical case of an iron-free serpentine rock is 3.62 GJ/t-CO2. This value can increase by 16 - 68% depending on the type of iron compound (FeO, Fe2O3 or Fe3O4) in the mineral. This suggests that the benefit from the potential use of FeOOH as an iron ore feedstock in iron and steelmaking should be determined by considering the energy, cost and emissions associated with the FeOOH by-product. AS recovery through crystallization is the second most energy intensive unit operation after the extraction reaction. However, the choice of mechanical vapor recompression (MVR) over the “simple evaporation” crystallization method has a potential energy savings of 15.2 GJ/t-CO2 (84 % savings). Integrating the Mg(OH)2 production method and the gas/solid carbonation process could provide up to an 25% energy offset to the CCM process energy requirements. Life cycle inventory assessment (LCIA) results show that for every ton of CO2 mineralized, the ÅAU CCM process avoids 430 - 480 kg CO2. The Mg(OH)2 process studied in this thesis has many promising features. Even at the current high energy and environmental burden, producing Mg(OH)2 from Mg-silicates can play a significant role in advancing CCM processes. However, dedicated future research and development (R&D) have potential to significantly improve the Mg(OH)2 process performance.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.