There had been a number of researches that investigated on the security market without transaction costs. The focus of this research is in the area that when the security market with transaction costs is fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal. The research approach adopted in this thesis includes linear algebra and elementary probability. The thesis provides evidence that we can maximize expected utility function to achieve our goal (maximize expected return under certain risk tolerance). The main conclusions drawn from this study are under certain conditions the security market is arbitrage-free, and we can always find an optimal portfolio maximizing certain expected utility function.

We define a novel algorithm based on utility functions for dynamically allocating tasks to mobile robots in a multi-robot system. The algorithm attempts to maximize the performance of the mobile robot while minimizing inter-robot communications. The algorithm takes into consideration the proximity of the mobile robot to the task, the priority of the task, the capability required by the task, the capabilities of the mobile robot, and the rarity of the capability within the population of mobile robots. We evaluate the proposed algorithm in a simulation study and compare it to alternative approaches, including the contract net protocol, an approach based on the knapsack problem, and random task selection. We find that our algorithm outperforms the alternatives in most metrics measured including percent of tasks complete, distance traveled per completed task, fairness of execution, number of communications, and utility achieved.

Stormwater user fees (SUFs) are an increasingly popular method of generating revenue for municipalities responsible for implementing complex stormwater regulations through the NPDES permit program. These fees can be created in a multitude of ways, including a flat fee for each parcel, charging by parcel area, charging based on a runoff factor, and many others. As a case study, eight SUFs were applied to the City of Roanoke and the Town of Blacksburg, both in Virginia, to determine the effect each SUF has on how land use type impacts the revenue composition. The City of Roanoke is larger and includes more industrial areas, but less multifamily impervious areas than Blacksburg, which translates differently in the SUFs. Residential parcels comprise the highest percentage of the revenue in all eight SUFs in Blacksburg and four in Roanoke. Open space parcels don't contain much impervious area yet account for up to 27% of the revenue. Industrial parcels comprise more of the revenue in Roanoke, averaging 11.1% compared to 4.6% in Blacksburg. A detailed digitized land cover dataset was compared to Blacksburg's land cover dataset, which resulted in maximum difference of $0.02 per parcel for residential parcel fees. Exemptions of large parcels in Roanoke, like the railroad and airport, if enacted would result in a maximum increase in fees of 15% and a shift of $7,491 of the monthly revenue to the residential parcels. / Master of Science

I analyzed the effects of Agriculture Risk Coverage (ARC) and Revenue Protection crop insurance (RP) on the RP coverage level by certainty equivalents and certainty equivalent returns. ARC is a commodity program that falls under Title I of the 2014 farm bill and triggers a payment for a participating producer once his actual revenue falls below a band of 76-86 percent of a calculated expected revenue. RP is a revenue-based crop insurance program that allows for a producer to sign up for one of eight different coverage levels ranging from 50-85 percent in 5 percent increments. This leads to the idea that in order to maximize his utility, a fully-informed, expected-utility maximizing producer should not choose to select full coverage RP but rather select the 75 percent RP and pair it with the ARC program. This analysis is conducted under the conceptual frameworks of expected-utility and cumulative prospect theory.

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