<p>Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics and Control, Volume 30, Issue 2006, Pages 843-877, with added details and background material in order to demonstrate the mathematical methods. In the investigation of the management of the investment portfolio, we only use one risky asset together with a bond and cash as other assets in a&nbsp / continuous time framework. The particular model is very much designed according to the members&rsquo / preference and then the funds are invested by the fund manager in the financial market. At the end, we are going to show various simulations of these models. Our methods include stochastic control for utility maximisation among others. The optimisation problem entails the optimal&nbsp / investment portfolio to maximise a certain power utility function. We use MATLAB and MAPLE programming languages to generate results in the form of graphs and tables</p>

With the obvious evolution and acceleration of smart grid, it is crucial for its success to rely on a solid transmission protocol among its peripherals due to its real time streaming. TCP is the well known traditional transport protocol used for a reliable transmission, and is a major player for smart grid. However, it lacks a fault tolerance transmission method that overcomes potential failures which may mitigate smart grid progress and in its turn decrease its reliability. We propose that smart grid operators utilize SCTP as the principle transport protocol for their smart grid communications, by using the two very significant characteristics offered by SCTP multi-homing and multi-streaming respectively. Thus, we argue that they can override two major obstacles caused by TCP Head of Line Blocking (HLB) and the inability of handling automatically two or more paths to a final destination. Although SCTP resembles TCP in many aspects, SCTP can definitely play a dominant role in many current and future applications due to its key features that do not exist in TCP. We have used ns2.34 simulator as the tool whom we relied on to investigate whether or not smart grid may benefit over TCP by the two SCTP features, and have analyzed the output of simulated results by using other analytical tools. As we obtain results, we argue that smart grid operators should rely on SCTP as a feasible transmission protocol instead of TCP.

While the market for credit instruments grew continuously in the decade before 2008, its liquidity has dried up significantly in the current crisis, and investors have become aware of the possible consequences of being exposed to credit risk. In this thesis we address these issues by pricing credit instruments using utility indifference pricing, a method that takes into account the investor's personal risk aversion and which is not affected by the lack of liquidity. Through stochastic optimal control methods, we use indifference pricing with exponential utility to determine corporate bond prices and CDS spreads. In the first part we examine how these quantities are affected by risk aversion under different models of default. The emphasis lies on a hybrid model, in which a regime switch of the reference entity is triggered by a creditworthiness index correlated to its stock price. The second part generalizes this setup by introducing uncertainty in the model parameters. Robust optimal control has been used independently in the literature to address model uncertainty for portfolio selection problems. Here, we incorporate this approach with utility indifference and derive some analytical and numerical results on how model uncertainty affects credit spreads.

While the market for credit instruments grew continuously in the decade before 2008, its liquidity has dried up significantly in the current crisis, and investors have become aware of the possible consequences of being exposed to credit risk. In this thesis we address these issues by pricing credit instruments using utility indifference pricing, a method that takes into account the investor's personal risk aversion and which is not affected by the lack of liquidity. Through stochastic optimal control methods, we use indifference pricing with exponential utility to determine corporate bond prices and CDS spreads. In the first part we examine how these quantities are affected by risk aversion under different models of default. The emphasis lies on a hybrid model, in which a regime switch of the reference entity is triggered by a creditworthiness index correlated to its stock price. The second part generalizes this setup by introducing uncertainty in the model parameters. Robust optimal control has been used independently in the literature to address model uncertainty for portfolio selection problems. Here, we incorporate this approach with utility indifference and derive some analytical and numerical results on how model uncertainty affects credit spreads.

This is a prospective, non-randomized pilot study comparing the cost-utility of hepatic resection, radiofrequency ablation (RFA), systemic chemotherapy, and symptom control only for the treatment of colorectal liver metastases. Seven patients underwent hepatic resection, 7 underwent RFA, 20 received chemotherapy, and 6 received symptom control alone. Liver resection provided an average of 2.51 QALY’s compared to 1.99 QALY’s for RFA, and 1.18 QALY’s for chemotherapy, and 0.82 QALY’s for symptom control alone. The costs were $20,122, $ 15,845, $15,069, and $3,899, respectively. The cost-utilities of liver resection and RFA were similar at $8,027 and $7,965 per QALY, respectively, although patients receiving RFA generally had more advanced disease. The cost-utility of chemotherapy was $12,751/QALY and the cost-utility of symptom control alone was $4,788/QALY. RFA is still a relatively new. However, if long-term survival proves promising, it may prove to be a viable alternative to liver resection. / May 2006

This dissertation combines three contributions to the literature on the determinants of well-being and the social nature of preferences. Departures from self-centred, consumption-oriented decision making are increasingly common in economic theory and are empirically well motivated by a wide range of behavioural data from experiments, surveys, and econometric inference. The first two contributions are focused on the idea that reference levels set by others’ consumption may figure prominently in both experienced well-being and in decision making. In the first paper, the well-being question is addressed empirically through the use of self-reported life satisfaction and high-resolution census and survey data in Canada. Strong income externalities are found at multiple spatial scales after controlling for various confounding factors. The second paper explores the general equilibrium consequences of a utility function having an explicit comparison with neighbours’ consumption. The question is investigated in a model in which decision makers knowingly choose their neighbours — and hence their consumption reference level — as well as their own consumption expenditure, thereby helping to set the reference level for nearby others. For both discrete and continuous distributions of types in an economy with a heterogeneous population undergoing such endogenous formation of consumption reference groups, there exist general equilibria in which differentiation of neighbourhoods occurs endogenously. The novel welfare implications of growth in such economies are described. The final paper addresses econometric reservations about the use of subjective reports as dependent variables. The date and location of survey interviews are combined with weather and climate records to construct the random component of weather conditions experienced by respondents on the day of their interview. Standard inferences about the determinants of life satisfaction remain robust after taking into account this significant source of affective bias.

Hydro One, a major distribution of electricity in Ontario, has reported that approximately 16,000 of the wood utility poles in its network of two million poles have been damaged by woodpeckers. With a cost of replacement of approximately $4000 per pole, replacing all affected poles is an expensive enterprise. Previous research conducted at UW attempted to quantify how different levels of woodpecker damage affected the pole strength. In the course of this research, some shear failures were observed. Utility poles being slender cantilevered structures, failures in shear are not expected. The objectives of this study were to determine the effective shear strength of wood utility poles and to determine the reliability of wood utility poles under different configurations, including poles that had been damaged by woodpeckers. An experimental programme was developed and conducted to determine the effective shear strength of wood poles. Red Pine wood pole stubs were used for this purpose. The stubs were slotted with two transverse half-depth cuts parallel to one another but with openings in opposite directions. A shear plane was formed between these two slots. The specimens were loaded longitudinally and the failure load was recorded and divided by the failure plane area to determine the shear strength. The moisture content of each specimen was recorded and used to normalize each data point to 12 % moisture content. The experimental study showed that the mean shear strength of the Red Pine specimens adjusted to 12 % moisture content was 2014 kPa (COV 47.5 %) when calculated using gross shear area, and 2113 kPa (COV 40.5 %) when calculated using net area. The shear strength of full-size pole specimens can be represented using a log-normal distribution with a scale parameter of λ = 0.5909 and a shape parameter of ζ = 0.5265. iii The reliability of Red Pine wood utility poles was determined analytically. A structural analysis model was developed using Visual Basic for Applications in Excel and used in conjunction with Monte Carlo simulation. Statistical distribution parameters for wind loads and ice accretion for the Thunder Bay, Ontario region were obtained from literature. Similarly, statistical data were obtained for the modulus of rupture and shear strength from previous research conducted at UW as well as the experimental programme conducted in this research. The effects of various properties on reliability were tested parametrically. Tested parameters included the height of poles above ground, construction grade, end- of-life criterion, and various levels of woodpecker damage. To evaluate the results of the analysis, the calculated reliability levels were compared to the annual reliability level of 98 % suggested in CAN/CSA-C22.3 No. 60826. Results of this reliability study showed that taller poles tend to have lower reliability than shorter ones, likely due to second-order effects having a greater influence on taller poles. The Construction Grade, a factor which dictates the load factors used during design, has a significant impact on the reliability of wood utility pole, with poles designed using Construction Grade 3 having a reliability level below the 98 % threshold. Poles designed based on Construction Grade 2 and 3 having reached the end-of-life criterion (60 % remaining strength) had reliability below this threshold whilst CG1-designed pole reliability remained above it. Wood poles with exploratory- and feeding-level woodpecker damage were found to have an acceptable level of reliability. Those with nesting-level damage had reliability below the suggested limits. Poles with feeding and nesting damage showed an increase in shear failure. The number of observed shear failure depended on the orientation of the damage. Woodpecker damage with the opening oriented with the neutral axis (i.e., the opening perpendicular to the direction of loading) produced a greater number of shear failure compared to woodpecker damage oriented with the extreme bending fibres.

A general methodology is described in which policyholder behaviour is decoupled from the pricing of a variable annuity based on the cost of hedging it, yielding two sequences of weakly coupled systems of partial differential equations (PDEs): the pricing and utility systems. The utility systems are used to generate policyholder withdrawal behaviour, which is in turn fed into the pricing systems as a means to determine the cost of hedging the contract. This approach allows us to incorporate the effects of utility-based pricing and factors such as taxation. As a case study, we consider the Guaranteed Lifelong Withdrawal and Death Benefits (GLWDB) contract. The pricing and utility systems for the GLWDB are derived under the assumption that the underlying asset follows a Markov regime-switching process. An implicit PDE method is used to solve both systems in tandem. We show that for a large class of utility functions, the two systems preserve homogeneity, allowing us to decrease the dimensionality of solutions. We also show that the associated control for the GLWDB is bang-bang, under which the work required to compute the optimal strategy is significantly reduced. We extend this result to provide the reader with sufficient conditions for a bang-bang control for a general variable annuity with a countable number of events (e.g. discontinuous withdrawals). Homogeneity and bang-bangness yield significant reductions in complexity and allow us to rapidly generate numerical solutions. Results are presented which demonstrate the sensitivity of the hedging expense to various parameters. The costly nature of the death benefit is documented. It is also shown that for a typical contract, the fee required to fund the cost of hedging calculated under the assumption that the policyholder withdraws at the contract rate is an appropriate approximation to the fee calculated assuming optimal consumption.

Over the past ten years, the State of California has realized environmental, economic, and social benefits through the increased deployment of solar photovoltaic technologies. However, utility-scale and residential-scale solar projects also pose a variety of problems, which have created barriers to their broader adoption. Community solar projects offer a model for solar development that can reduce the problems associated with utility-scale and residential-scale projects, while simultaneously preserving the benefits of each. This thesis examines the problems associated with current solar projects and proposes policy to support the community solar project model in California.

The objective of the master’s thesis work is to investigate how an autonomous underwater vehicle (AUV) should act in an underwater tunnel environment. The thesis proposes sensors, control strategies, mission statement, among others, required for tunnel assignments. A behavior-based control (BBC) strategy has been developed to control the AUV. The BBC is used in the middle level of the vehicle control, i.e. the reactive control system which describes how the AUV navigates through a tunnel, while other events are considered. The control strategy has also been separated into two parts, and these are: controlling the AUV’s heading and controlling the AUV to a desired distance from the tunnel wall. To be able to evaluate the performance of the system, a graphical user interface (GUI) has been developed. The GUI enables the operator to change control settings during simulations. Two proposed control strategies are presented with simulated results. / Syftet med examensarbetet är att undersöka hur en autonom undervattensfarkost (AUV) bör agera i en undervattenstunnel miljö. Avhandlingen föreslår sensorer, reglerstrategier, uppdragsbeskrivning med mera som krävs för tunneluppdrag. En beteendebaserad (behavior-based) reglerstrategi har utvecklats för att styra AUV:n. Reglerstrategin används i mellersta nivån i farkostens reglering, det vill säga den reaktiva regleringen som beskriver hur farkosten ska styra genom en tunnel samtidigt som andra händelser beaktas. Reglerstrategin har även delats upp i två delar: reglering av AUV:ns kurs och reglering av AUV:n till ett önskat avstånd från tunnelns vägg. För att kunna verifiera funktionaliteten av systemet så har även ett grafiskt användargränssnitt utvecklats. Gränssnittet möjliggör att man kan ändra reglerparametrar under en simulering. Två föreslagna reglerstrategier presenteras med tillhörande resultat.