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In this thesis, we study several utility maximisation problems under model uncertainty, involving optimal investment, valuation and hedging. We first derived martingale distortion representations for classical utility maximisation problems in a non-Markovian stochastic factor model, with power, logarithmic and exponential utilities. We then study multiple priors power utility maximisation problems when the reference model is a non-Markovian stochastic factor model, and derive a BSDE representation of the value process, optimal strategy and least favourable model. We also study a variational preferences logarithmic utility maximisation problem when the reference model is a non-Markovian stochastic factor model, and when the plausible models are penalised by an additive entropic penalty function. The robust problem is transferred to a classical utility maximisation problem with a power utility whose risk aversion is dependent on the model ambiguity aversion parameter. We then fully solve the robust problem and perform numerical tests comparing several classical and robust strategies for a Stein-Stein stochastic volatility model and for a Heston model. Finally, we study robust exponential valuation and hedging problems in a basis risk model, using both the multiple priors approach and the variational preferences approach with a multiplicative penalty function. Specialising to a constant parameter basis risk model, the robust problems admit explicit or approximate solutions, thus we are able to conduct large-scale simulation based tests on performances of various pricing and hedging strategies.

Bayesian analysis of full waveform laser detection and ranging (LaDAR) signals using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms have shown higher estimation accuracy, resolution and sensitivity to detect weak signatures for 3D surface profiling, and construct multiple layer images with varying number of surface returns. However, it is computational expensive. Although parallel computing has the potential to reduce both the processing time and the requirement for persistent memory storage, parallelizing the serial sampling procedure in RJMCMC is a significant challenge in both statistical and computing domains. While several strategies have been developed for Markov chain Monte Carlo (MCMC) parallelization, these are usually restricted to fixed dimensional parameter estimates, and not obviously applicable to RJMCMC for varying dimensional signal analysis. In the statistical domain, we propose an effective, concurrent RJMCMC algorithm, state space decomposition RJMCMC (SSD-RJMCMC), which divides the entire state space into groups and assign to each an independent RJMCMC chain with restricted variation of model dimensions. It intrinsically has a parallel structure, a form of model-level parallelization. Applying the convergence diagnostic, we can adaptively assess the convergence of the Markov chain on-the-fly and so dynamically terminate the chain generation. Evaluations on both synthetic and real data demonstrate that the concurrent chains have shorter convergence length and hence improved sampling efficiency. Parallel exploration of the candidate models, in conjunction with an error detection and correction scheme, improves the reliability of surface detection. By adaptively generating a complimentary MCMC sequence for the determined model, it enhances the accuracy for surface profiling. In the computing domain, we develop a data parallel SSD-RJMCMC (DP SSD-RJMCMCU) to achieve efficient parallel implementation on a distributed computer cluster. Adding data-level parallelization on top of the model-level parallelization, it formalizes a task queue and introduces an automatic scheduler for dynamic task allocation. These two strategies successfully diminish the load imbalance that occurred in SSD-RJMCMC. Thanks to the coarse granularity, the processors communicate at a very low frequency. The MPIbased implementation on a Beowulf cluster demonstrates that compared with RJMCMC, DP SSD-RJMCMCU has further reduced problem size and computation complexity. Therefore, it can achieve a super linear speedup if the number of data segments and processors are chosen wisely.

E-waste is an emerging issue driven by the rapidly increasing quantities, the hazards involved and the valuable materials in it. Due to a lack of environmentally sound technologies or equipment and the imperfect e-waste management system, the poor quality e-waste recycling and disposal methods commonly practiced in developing countries now have serious and hazardous effects on the environment and the workers'/residents' health. Additionally, industrialized countries are exporting increasing quantities of e-waste to developing countries, complicating the situation finther. The environmental and health issues caused by e-waste in developing countries have resulted in the search for solutions to address this problem before it becomes worse. The main purpose of this research is to find how legislation and regulations be used to improve management of e-waste in developing countries especially studying a case in China on e-waste management, which is a very helpful example to other developing countries which are also facing the same e-waste'issue. A case study methodology was used in this research. To collect data, semi-structured interviews with officers or experts from key relevant government departments/institutions involved in e-waste management/regulation, from electronic appliance producers, from customers at different levels of the value chain, as well as direct and non-participant observations were carried out in six cities of China. For another perspective, the review of relevant departmental documents/publications was also carried out to multiply the source of data. In this case study the analysis relies largely on qualitative data and interpretive methods, applied to what was found in interviews/observations and what is written down in documents/ literatures. The research found that lack of systernatic and enforceable law and regulations has become the most serious obstacle in the e-waste management system and limited the effective control of e-waste in developing countries. Developing subsidiary regulations and standards could support the enforcement of the main national law and regulations on e-waste management and it could farther urge the development of local regulations to improve the enforceýbility of the national law and regulations. Identifying the principal administrative department and coordinating the cooperation of various departments could avoid the duplication of administrative functions among government departments. It is important to construct monitoring systems to supervise the enforcement of the regulations and construct the standards and registration system to qualify the e-waste recycling and disposal enterprises, the secondhand market of electronic products and the regenerative resources market of reusable materials in ewaste. The economic differences made it possible to formulate special regulations for economically backward areas compared to the, more advanced areas even within one country. Improving the existing e-waste recovery system and regulating the payment system according to the local economic conditions for e-waste recycling and disposal could improve the integrated management of e-waste. Producers as well as government and even consumers should be responsible for e-waste together. The government needs to continuously strengthen regulatory systems to ensure that the huge economic benefits from the e-waste recycling industry are not overshadowed by the negative impact on the workers'/residents' welfare and overall environmental sustainability,