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This paper investigates optimal portfolio strategies in a market with partial information on the drift. The drift is modelled as a function of a continuous-time Markov chain with finitely many states which is not directly observable. Information on the drift is obtained from the observation of stock prices. Moreover, expert opinions in the form of signals at random discrete time points are included in the analysis. We derive the filtering equation for the return process and incorporate the filter into the state variables of the optimization problem. This problem is studied with dynamic programming methods. In particular, we propose a policy improvement method to obtain computable approximations of the optimal strategy. Numerical results are presented at the end. (author's abstract)

An optimal stochastic multi-crop irrigation scheduling algorithm was developed which was able to incorporate complex farm system models, and constraints on daily and seasonal water use, with the objective of maximising farm profit. This scheduling method included a complex farm simulation model in the objective function, used decision variables to describe general management decisions, and used a custom heuristic method for optimisation. Existing optimal schedulers generally use stochastic dynamic programming which relies on time independence of all parameters except state variables, thereby requiring over-simplistic crop models. An alternative scheduling method was therefore proposed which allows for the inclusion of complex farm system models. Climate stochastic properties are modelled within the objective function through the simulation of several years of historical data. The decoupling of the optimiser from the objective function allows easy interchanging of farm model components. The custom heuristic method, definition of decision variables, and use of the Markov chain equation (relating an irrigation management strategy to mean water use) considerably increases optimisation efficiency. The custom heuristic method used simulated annealing with continuous variables. Two extensions to this method were the efficient incorporation of equality constraints and utilisation of population information. A case study comparison between the simulated annealing scheduler and scheduling using stochastic dynamic programming, using a simplistic crop model, showed that the two methods resulted in similar performance. This demonstrates the ability of the simulated annealing scheduler to produce close to optimal schedules. A second case study demonstrates the ability of the simulated annealing scheduler to incorporate complex farm system models by including the FarmWi$e model by CSIRO in the objective function. This case study indicates that under conditions of limited seasonal water, the simulated annealing scheduler increases pasture yield returns by an average of 10%, compared with scheduling irrigation using best management practice. Alternatively expressed, this corresponds to a 20-25% reduction in seasonal water use (given no change in yield return).

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The aim of this thesis is to first give a brief review of waiting line problems which often is a subject related to queueing theory. Simple counting processes such as the Poisson process and the duration of service time of each customer being exponentially distributed are often taught in a undergraduate or graduate stochastic process course. In this thesis, we will continue discussing such waiting line problems with priority assignment on each customer. This type of queueing processes are called priority queueing models. Patients requiring ER service are triaged and the order of providing service to patients more than often reflects early symptoms and complaints than final diagnoses. Triage systems used in hospitals vary from country to country and region to region. However, the goal of using a triage system is to ensure that the sickest patients are seen first. Such wait line system is much comparable to a priority queueing system in our study. The finite Markov chain imbedding technique is very effective in obtaining the waiting time distribution of runs and patterns. Applying this technique, we are able to obtain the probability distribution of customer wait time of priority queues. The results of this research can be applied directly when studying patient wait time of emergency medical service. Lengthy ER wait time issue often is studied from the view of limited spacing and complications in hospital administration and allocation of resources. In this thesis, we would like to study priority queueing systems by mathematical and probabilistic modeling.

We present a Markov chain analysis for studying the performance of wireless ad hoc networks. The models presented in this dissertation support an arbitrary backoff strategy. We found that the most important parameter affecting the performance of binary exponential backoff is the initial backoff window size. Our experimental results show that the probability of collision can be reduced when the initial backoff window size equals the number of terminals. Thus, the throughput of the system increases and, at the same time, the delay to transmit the frame is reduced. In our second contribution, we present a new analytical model of a Medium Access Control (MAC) layer for wireless ad hoc networks that takes into account frame retry limits for a four-way handshaking mechanism. This model offers flexibility to address some design issues such as the effects of traffic parameters as well as possible improvements for wireless ad hoc networks. It effectively captures important network performance characteristics such as throughput, channel utilization, delay, and average energy. Under this analytical framework, we evaluate the effect of the Request-to-Send (RTS) state on unsuccessful transmission probability and its effect on performance particularly when the hidden terminal problem is dominant, the traffic is heavy, or the data frame length is very large. By using our proposed model, we show that the probability of collision can be reduced when using a Request-to-Send/Clear- to-Send (RTS/CTS) mechanism. Thus, the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. In our third contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account channel bit errors and frame retry limits for a two-way handshaking mechanism. This model offers flexibility to address design issues such as the effects of traffic parameters and possible improvements for wireless ad hoc networks. We illustrate that an important parameter affecting the performance of binary exponential backoff is the initial backoff window size. We show that for a low bit error rate (BER) the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. Results show also that the negative acknowledgment-based (NAK-based) model proves more useful for a high BER. In our fourth contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account Quality of Service (QoS) of the MAC layer for a two-way handshaking mechanism. The model includes a high priority traffic class (class 1) and a low priority traffic class (class 2). Extension of the model to more QoS levels is easily accomplished. We illustrate an important parameter affecting the performance of an Arbitration InterFrame Space (AIFS) and small backoff window size limits. They cause the frame to start contending the channel earlier and to complete the backoff sooner. As a result, the probability of sending the frame increases. Under this analytical framework, we evaluate the effect of QoS on successful transmission probability and its effect on performance, particularly when high priority traffic is dominant. / Graduate

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This study tests the size effect in the London Stock Exchange, using data for all nonfinancial listed firms from January 1985 to December 1995. The initial tests indicate that average stock returns are negatively related to firm size and that small firm portfolios earn returns in excess of the market risk. Further, the study tests whether the size effect is a proxy for variables such as the Book-to- Market Value and the Borrowing Ratio, as well as the impact of the dividend and the Bid- Ask spread on the return of the extreme size portfolios. The originality of this study is in the application of the Markov Chain Model to testing the Random Walk and Bubbles hypotheses, and the Vector Autoregression (VAR) framework for testing the relationship of macroeconomic variables with size portfolio returns.