http://hdl.handle.net/2440/5132 2013-05-25T20:37:08Z http://hdl.handle.net/2440/74759 Title: Existence, uniqueness and comparisons for BSDEs in general spaces Author: Cohen, Samuel Nicholas; Elliott, Robert James Abstract: We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones.We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces. 2011-12-31T13:30:00Z http://hdl.handle.net/2440/74745 Title: A Bayesian approach for optimal reinsurance and investment in a diffusion model Author: Zhang, Xin; Elliott, Robert James; Siu, Tak Kuen Abstract: A Bayesian adaptive control approach to the combined optimal investment/reinsurance problem of an insurance company is studied. The insurance company invests in a money market and a capital market index with an unknown appreciation rate, or “drift”. Using a Bayesian approach, the unknown drift is described by an unobservable random variable with a known (prior) probability distribution. We assume that the risk process of the company is governed by a diffusion approximation to the compound Poisson risk process. The company also purchases reinsurance. The combined optimal investment/reinsurance problem is formulated as a stochastic optimal control problem with partial observations. We employ filtering theory to transform the problem into one with complete observations. The control problem is then solved by the dynamic programming Hamilton–Jacobi–Bellman (HJB) approach. Semi-analytical solutions are obtained for the exponential utility case. 2011-12-31T13:30:00Z http://hdl.handle.net/2440/74724 Title: Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution Author: Chen, Qian; Gerlach, Richard; Lu, Zudi Description: 1st issue of the Annals of Computational and Financial Econometrics. Sixth Special Issue on Computational Econometrics. 2011-12-31T13:30:00Z http://hdl.handle.net/2440/41879 Title: Factors affecting survival after endovascular aneurysm repair: results from a population based audit Author: Boult, Maggi; Maddern, Guy John; Barnes, M.; Fitridge, Robert A. Abstract: Objectives: To determine the effect of pre-operative factors on mid-term survival of patients enrolled in an Australian audit of endovascular aneurysm repair (EVAR). Design: Prospective longitudinal national register (audit) of patients undergoing EVAR. Methods: 961 individuals who had elective or semi-urgent EVAR of abdominal aortic aneurysms were enrolled in the audit between November 1999 and May 2001. Data was contributed by 81 surgeons from 64 hospitals. Kaplan-Meier survival analysis was used to determine survival rates and factors significantly influencing survival. Parametric survival analysis with log-exponential distribution was used to estimate expected 3 and 5 year survival for different ages, ASA, creatinine and aneurysm sizes. Results: Overall survival was 93% at 1 year, 80% at 3 years and 67% at five years. Survival rates were found to be statistically associated with ASA, age, aneurysm size and creatinine levels. ASA has the largest effect. Five year survival rates for aneurysms ≥65 mm and <55 mm were 54% and 76% respectively. Pre-operative creatinine levels ≥ 160 μmol/L lowered the survival rate from 71% to 40%. Conclusions: Survival for EVAR patients is strongly correlated with a number of pre-operative factors. This survival analysis provides a useful decision-making tool for surgeons particularly for individuals with smaller aneurysms. Description: Copyright © 2007 Elsevier Ltd All rights reserved. 2006-12-31T13:30:00Z