Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in finance is developed, with application to asset allocation. The numerical scheme has the following properties: it is unconditionally stable; convergence to the viscosity solution is guaranteed; there are no restrictions on the underlying stochastic process; it can be easily extended to include features as needed such as uncertain volatility and transaction costs; and central differencing is used as much as possible so that use of a locally second order method is maximized. In this thesis, continuous time mean variance type strategies for dynamic asset allocation problems are studied. Three mean variance type strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic variation, are investigated. The numerical method can handle various constraints on the control policy. The following cases are studied: allowing bankruptcy (unconstrained case), no bankruptcy, and bounded control. In some special cases where analytic solutions are available, the numerical results agree with the analytic solutions. These three mean variance type strategies are compared. For the allowing bankruptcy case, analytic solutions exist for all strategies. However, when additional constraints are applied to the control policy, analytic solutions do not exist for all strategies. After realistic constraints are applied, the efficient frontiers for all three strategies are very similar. However, the investment policies are quite different. These results show that, in deciding which objective function is appropriate for a given economic problem, it is not sufficient to simply examine the efficient frontiers. Instead, the actual investment policies need to be studied in order to determine if a particular strategy is applicable to specific investment problem.

Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in finance is developed, with application to asset allocation. The numerical scheme has the following properties: it is unconditionally stable; convergence to the viscosity solution is guaranteed; there are no restrictions on the underlying stochastic process; it can be easily extended to include features as needed such as uncertain volatility and transaction costs; and central differencing is used as much as possible so that use of a locally second order method is maximized. In this thesis, continuous time mean variance type strategies for dynamic asset allocation problems are studied. Three mean variance type strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic variation, are investigated. The numerical method can handle various constraints on the control policy. The following cases are studied: allowing bankruptcy (unconstrained case), no bankruptcy, and bounded control. In some special cases where analytic solutions are available, the numerical results agree with the analytic solutions. These three mean variance type strategies are compared. For the allowing bankruptcy case, analytic solutions exist for all strategies. However, when additional constraints are applied to the control policy, analytic solutions do not exist for all strategies. After realistic constraints are applied, the efficient frontiers for all three strategies are very similar. However, the investment policies are quite different. These results show that, in deciding which objective function is appropriate for a given economic problem, it is not sufficient to simply examine the efficient frontiers. Instead, the actual investment policies need to be studied in order to determine if a particular strategy is applicable to specific investment problem.

Research on persuasive technologies for promoting healthy behaviours has been surging in recent years, but these technologies have the risk of being perceived as undesirable meddling. The current study puts forward a non-coercive and libertarian paternalistic alternative - the nudge theory. The foundation of the nudge theory is informed by the dual processing theory and can be categorized in two types - Type 1 nudging and Type 2 nudging. As design tools, two Type 1 nudging methods: default setting and manipulation of accessibility; and four Type 2 nudging methods: reminders, prompts, framing and precommitment strategies were selected to be featured. Sleep was chosen as the use case for this study, for it is associated with a number of non-communicable diseases yet considerably few studies of persuasive technology are about sleep. Better sleep hygiene is a significant means to improve sleep, therefore used as the design goal. The current study explores possible solutions for persuasive technologies for improving sleep hygiene, and better understand the design potentials and the persuasive characteristics of different types and methods of nudging. The research methodology is informed by scenario-based design. Five (four male and one female) academic professionals with backgrounds in interaction design, human-computer interaction, artificial intelligence and robotics took part in the study. Seven scenarios and thirteen prototypes were created to illustrate the situations and present the possible solutions. Results also showed that Type 1 nudging is considered more convenient and effective. However, the sense of control is better preserved in Type 2 nudging. In regard to nudging methods, default setting is considered as the most eective method under the condition of goal-alignment, but prone to error. Manipulation of accessibility should be designed so that the navigation is intuitive and the integrity of availability should not be damaged. Timing is the most prominent factor for reminders, and the influence of reminders could be reinforced by prioritizing and cross-platform availability. The presence of prompts could be emphasized by purposeful placement, and appropriateness should be considered. The perception of framing is highly subjective, therefore it should be user-tailored and context-aware. The effects of precommitment strategies are able to access higher-level motivation, but should be reinforced with other methods. To summarize the design principles, when designing nudges in persuasive technologies, the following factors should be considered: goal alignment, intuitiveness, context awareness, availability and accessing motivation. / Forskning inom temat persuasive teknologi för hälsoinriktade beteenden har ökat under den senaste tiden. Dock kan sådana teknologier oftast uppfattas som en oönskad inblandning i människors privata liv. Denna studie föreslår ett otvingade och libertarianskt paternalistiskt alternativ för att påverka val och beteenden – nudge teorin. Flera tidigare beprövade designverktyg betonas i denna teori. Nudge teorin har en dual process teoretisk bakgrund och kan delas in i två typer av nudging –- Typ 1 nudging och Typ 2 nudging. Bland Typ 1 verktyg väljs default setting och manipulation of accessibility, och bland Typ 2 metoder väljs reminders, prompts, framing och pre-commitment strategies. I syfte att illustrera detta användes sömn som exempel, då det har länkats till flera icke-smittsamma sjukdomar och få studier har försökt att undersöka motiverande design i relation till sömn. Bättre sömnhygien är ett betydelsefullt verktyg för att förbättra sömn och användes därför som målsättning. Denna studie undersöker möjliga alternativ för persuasive teknologi i syfte att förbättra sömn. Dessutom undersöktes potentialen av olika typer av persuasive teknologi och metoder för nudging. Den valda metodologi är en informerad scenariobaserad design. Fem akademiskt anställda, fyra män och en kvinna, med bakgrund inom interaction design, human-computer interaction, artificial intelligence och robotics, deltog i denna studie. Sju scenarion och tretton prototyper utarbetades för att illustrera en situation och presentera en möjlig lösning där sömnhygien kunde förbättras igenom persuasive teknologi. Resultaten visade att Typ 1 nudging ansågs vara mer lämpligt och effektiv. Emellertid bibehålls känslan av kontroll mer inom Typ 2 nudging. Default setting ansågs som mest effektiv inom betingelsen goal alignment, men med risk för bakslag. Manipulation of accessibility bör designas så att navigering är intuitiv och att integriteten av tillgänglighet inte störs. Tajming är den mest framträdande faktorn för reminders och deras påverkan skulle kunna framhävas igenom prioritering och cross-platform availability. Prompts skulle kunna framhävas mer igenom igenomtänkt placering där lämplighet är en drivande faktor. Uppfattningen av framing är mycket subjektiv och bör vara anpassad till användaren. Pre-commitment strategier har tillgång till högre motivation men bör förstärkas med andra medel.

本研究從2009-2010全國成人煙草使用率的調查數據，研討不同類型的戒菸方式對於個體行為異質性所造成的影響。先前的研究顯示有意願想要戒菸的吸菸者有外部戒菸控制方式的需求，然而我們無法在有限的研究中找出相同的吸煙者不滿意對於外部戒菸的控制需求。此外我們發現，高成癮率和高程度的吸菸量提高吸煙者對尼古丁替代物或其他藥物的需求。我們在這份研究中甚至發現，無知的雙曲線貼現吸煙者降低外部需求的戒菸者對於禁煙令或香煙稅當中的關係。 / Using data from the 2009-2010 National Adult Tobacco Survey, this study investigates how the heterogeneity of individual behaviors affects demand for different types of cessation supports. Previous studies have demonstrated that smokers with a desire to quit have a demand for external cessation controls, however, there is limited research into how those same smokers demand individual disutility decreasing supports like nicotine replacement or counseling. We find that high addiction and consumption levels increase the demand for nicotine replacement or other medication. We also find support linking naïf hyperbolic discounters to lower demand for external cessation supports like smoking bans or cigarette taxes.