On the distribution of the time to ruin and related topics

Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8

Is valve-sparing aortic root replacement better than total aortic root replacement? An overview of reviews

BackgroundTotal aortic root replacement (TRR) is certainly beneficial for aortic root disease, but does it still have an advantageous prognosis for patients compared to valve-sparing aortic root replacement (VSRR)? An overview of reviews was conducted to assess each of their clinical efficacy/effectiveness.Review methodsSystematic reviews (SRs)/Meta-analyses comparing the prognosis of TRR and VSRR in aortic root surgery were collected from 4 databases, all searched from the time of database creation to October 2022. Two evaluators independently screened the literature, extracted information and applied the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement, A Measurement Tool to Assess Systematic Reviews 2 (AMSTAR 2) tool, Grading of Recommendations, Assessment, Development and Evaluations (GRADE), and Risk of Bias in Systematic Reviews (ROBIS) to evaluate the quality of reporting, methodological quality, risk of bias, and level of evidence of the included studies.Main resultsA total of 9 SRs/Meta-analyses were ultimately included. In terms of the reporting quality of the included studies, PRISMA scores ranged from 14 to 22.5, with issues mainly in reporting bias assessment, risk of study bias, credibility of evidence, protocol and registration, and funding sources. The methodological quality of the included SRs/Meta-analyses was generally low, with key items 2, 7, and 13 having major flaws and non-key items 10, 12, and 16. In terms of risk of bias assessment, the overall assessment of the included 9 studies was high-risk. The quality of the evidence was rated as low to very low quality for the three outcome indicators selected for the GRADE quality of evidence rating: early (within 30 days postoperatively or during hospitalization) mortality, late mortality, and valve reintervention rate.ConclusionsVSRR has many benefits including reduced early and late mortality after aortic root surgery and reduced rates of valve-related adverse events, but the methodological quality of the relevant studies is low, and there is a lack of high-quality evidence to support this.Systematic Review Registrationhttps://www.PROSPERO, identifier: CRD42022381330

Bayesian Calibration of AquaCrop Model for Winter Wheat by Assimilating UAV Multi-Spectral Images

Crop growth model plays a paramount role in smart farming management, which not only provides quantitative information on crop development but also evaluates various management strategies. A reliable model is desirable but challenging due to the presence of unknown and uncertain parameters; therefore, crop model calibration is significant to achieve its potentials. This work is focused on the calibration of AquaCrop model by leveraging advanced Bayesian inference algorithms and UAV multi-spectral images at field scales. In particular, aerial images with high spatial- temporal resolutions are first applied to obtain Canopy Cover (CC) value by using machine learning based classification. The CC is then assimilated into AquaCrop model and uncertain parameters could be inferred by Markov Chain Monte Carlo (MCMC). Both simulation and experimental validation are performed. The experimental aerial images of winter wheat at Yangling district from Oct/2017 to June/2018 are applied to validate the proposed method against the conventional optimisation based approach by Simulated Annealing (SA). 100 Monte Carlo simulations show that the root mean squared error (RMSE) of Bayesian approach yields a smaller parameter estimation error than optimisation approach. While the experimental results show that: (i) a good wheat/background classification result is obtained for the accurate calculation of CC; (ii) the predicted CC values by Bayesian approach are consistent with measurements by 4-fold cross validation, where the RMSE is 0.0271 smaller than optimisation approach (0.0514); (iii) in addition to parameter estimation, their distribution information is also obtained in the developed Bayesian approach, reflecting the prediction confidence. It is believed that the Bayesian model calibration, although is developed for AquaCrop model, can find a wide range of applications to various simulation models in agriculture and forestry

Insight-HXMT observations of Swift J0243.6+6124 during its 2017-2018 outburst

The recently discovered neutron star transient Swift J0243.6+6124 has been monitored by {\it the Hard X-ray Modulation Telescope} ({\it Insight-\rm HXMT). Based on the obtained data, we investigate the broadband spectrum of the source throughout the outburst. We estimate the broadband flux of the source and search for possible cyclotron line in the broadband spectrum. No evidence of line-like features is, however, found up to $\rm 150~keV$. In the absence of any cyclotron line in its energy spectrum, we estimate the magnetic field of the source based on the observed spin evolution of the neutron star by applying two accretion torque models. In both cases, we get consistent results with $B\rm \sim 10^{13}~G$, $D\rm \sim 6~kpc$ and peak luminosity of $\rm >10^{39}~erg~s^{-1}$ which makes the source the first Galactic ultraluminous X-ray source hosting a neutron star.Comment: publishe

Application of Joint Inversion of Different Electrode Arrays in Ancient Mausoleum Detection

Electrical resistivity tomography is a popular geophysical method and has been applied in shallow exploration, involving hydrology, archaeology, and geology, in recent years. To enhance the resolution of electrical resistivity tomography and deal with complex geological settings, we propose the weighted combined inversion of different electrode arrays based on the Jacobian matrix, and then, taking Wenner and dipole-dipole datasets as examples, test its effectiveness on synthetic models and a field case of detecting ancient mausoleum. The results show that the resolution of the weighted combined inversion results is superior to that of a single electrode array in transverse and longitudinal directions, and in the field case, it is demonstrated that the weighted combined inversion algorithm can alleviate the inherent defects of U-shaped electrode array, reduce the ambiguity of inversion, and better constrain the width of the mausoleum