Omega risk model with tax

In this paper we study the Omega risk model with surplus-dependent tax payments in a time-homogeneous diffusion setting. The new model incorporates practical features from both the Omega risk model(Albrecher and Gerber and Shiu (2011)) and the risk model with tax(Albrecher and Hipp (2007)). We explicitly characterize the Laplace transform of the occupation time of an Azema-Yor process(e.g. a process refracted by functionals of its running maximum) below a constant level until the first hitting time of another Azema-Yor process or until an independent exponential time. This result unifies and extends recent literature(Li and Zhou (2013) and Zhang (2014)) incorporating some of their results as special cases. We explicitly characterize the Laplace transform of the time of bankruptcy in the Omega risk model with tax and discuss an extension to integral functionals. Finally we present examples using a Brownian motion with drift

Energy use and indoor environment in a sample of monitored domestic buildings in the UK

This paper is based on the low-cost approaches and transferable techniques that were applied in a PhD reserch project on energy-related occupancy activities. The strengths of qualitative and quantitative research strategies were combined for the study of this socio-technical research topic. Long-term field measurement was conducted for data acquisition using self-configured monitoring schemes. Case study was selected as the research approach. Building characteristics and household features in each case study group were purposefully selected to deploy same-standard monitoring schemes. Comparable monitoring results were pre-processed following identical procedures to implement the selected data analysis methods. The inspection results provided the researcher and the associated project partners with a novel perspective to interpret the difference in actual energy consumption and indoor environment within and between the case study groups. The research methodology and moitoring approach are covered in this paper that also presents the macro-scale monitoring results of energy use and indoor environment in two case study groups. The micro-scale presentation and algorithm-based examination will be covered in other academic papers. This paper demonstrates the huge potential for some commonly applied building assessment methods to be improved by objectively considering currently overlooked aspects, such as the low-tech design and construction of heavy-weight thermal mass houses and the largely varied occupancy activities. Future work relating to the comparison of actual monitoring data with simulation results is pointed out at the end of the paper

Stochastic areas of diffusions and applications in risk theory

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform of the stochastic area in terms of the eigenfunctions of the associated diffusion. We also explicitly obtain the integer moments of the stochastic area in terms of scale and speed densities of the associated diffusion. Specifically we study in detail three stopping times: the first passage time to a constant level, the first drawdown time and the Azema-Yor stopping time. We also study the total occupation area of the diffusion below a constant level. We show applications of the results to a new structural model of default (Yildirim 2006), the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang 2012), and a diffusion risk model with surplus-dependent tax (Albrecher and Hipp 2007, Li, Tang and Zhou 2013)