Some Stochastic Optimization Problems in Reinsurance and Insurance

Insurance, which hedges against the risk of a contingent loss, is an indispensable risk management tool for both institutions and individuals. Reinsurance, namely, a form of insurance accessible to insurers, helps limit the liability of an insurer on certain set of risks and protect against catastrophic events, while various insurance products are available for individuals to cover uncertain losses from almost every aspect of their daily life. This thesis focuses on dynamically controlling the utilities of decision makers by imposing various controls, including reinsurance for insurers, and life annuity and term life insurance for individuals, either analytically or numerically. Utilizing (re)insurance to attain certain objectives has long been a central focus in the actuarial science literature. This thesis aims at making contributions in the existing literature by applying models that are more in line with reality, both in regard to the underlying dynamic models and control variables. In Chapter 3, we study the optimal reinsurance-investment strategy for dynamic contagion claims. Such a claim process no longer possesses the stationary and independent increment property, and can capture contagion due to endogenous (self-exciting) and exogenous (externally-exciting) factors. Adopting the time-consistent mean-variance criterion, we analytically solve for the equilibrium strategies and analyze the impact of some contagion factors on the resulting optimal reinsurance strategies. Chapter 4 models the basic surplus process as a spectrally negative Lévy process, and focuses on the partial information of the unobservable stock return rate to look into the optimal reinsurance-investment problem under the time-consistent mean-variance criterion. Analytical solutions are obtained by solving an extended HJB equation, and hedging demand due to partial information is carefully studied. Chapter 5 is devoted to the study of the optimal allocation of life annuity, term life insurance and consumption for an individual under a general force of mortality. In our setup, an individual's decision of life annuity, term life insurance and consumption are allowed to depend on the current wealth, existing life annuity and existing term life insurance, and realistic lump-sum purchases are considered. Assuming a CRRA preference, a penalty method is applied to numerically solve for the optimal allocations of wealth in life annuity, term life insurance and consumption. To ensure that the thesis flows smoothly, Chapter 1 introduces the background literature and main motivations of this thesis. Chapter 2 is devoted to mathematical preliminaries for the latter chapters. Finally, Chapter 6 concludes the thesis with potential directions for future research

Root Hair Single Cell Type Specific Profiles of Gene Expression and Alternative Polyadenylation Under Cadmium Stress

Transcriptional networks are tightly controlled in plant development and stress responses. Alternative polyadenylation (APA) has been found to regulate gene expression under abiotic stress by increasing the heterogeneity at mRNA 3′-ends. Heavy metals like cadmium pollute water and soil due to mining and industry applications. Understanding how plants cope with heavy metal stress remains an interesting question. The Arabidopsis root hair was chosen as a single cell model to investigate the functional role of APA in cadmium stress response. Primary root growth inhibition and defective root hair morphotypes were observed. Poly(A) tag (PAT) libraries from single cell types, i.e., root hair cells, non-hair epidermal cells, and whole root tip under cadmium stress were prepared and sequenced. Interestingly, a root hair cell type-specific gene expression under short term cadmium exposure, but not related to the prolonged treatment, was detected. Differentially expressed poly(A) sites were identified, which largely contributed to altered gene expression, and enriched in pentose and glucuronate interconversion pathways as well as phenylpropanoid biosynthesis pathways. Numerous genes with poly(A) site switching were found, particularly for functions in cell wall modification, root epidermal differentiation, and root hair tip growth. Our findings suggest that APA plays a functional role as a potential stress modulator in root hair cells under cadmium treatment

Video-driven Neural Physically-based Facial Asset for Production

Production-level workflows for producing convincing 3D dynamic human faces have long relied on an assortment of labor-intensive tools for geometry and texture generation, motion capture and rigging, and expression synthesis. Recent neural approaches automate individual components but the corresponding latent representations cannot provide artists with explicit controls as in conventional tools. In this paper, we present a new learning-based, video-driven approach for generating dynamic facial geometries with high-quality physically-based assets. For data collection, we construct a hybrid multiview-photometric capture stage, coupling with ultra-fast video cameras to obtain raw 3D facial assets. We then set out to model the facial expression, geometry and physically-based textures using separate VAEs where we impose a global MLP based expression mapping across the latent spaces of respective networks, to preserve characteristics across respective attributes. We also model the delta information as wrinkle maps for the physically-based textures, achieving high-quality 4K dynamic textures. We demonstrate our approach in high-fidelity performer-specific facial capture and cross-identity facial motion retargeting. In addition, our multi-VAE-based neural asset, along with the fast adaptation schemes, can also be deployed to handle in-the-wild videos. Besides, we motivate the utility of our explicit facial disentangling strategy by providing various promising physically-based editing results with high realism. Comprehensive experiments show that our technique provides higher accuracy and visual fidelity than previous video-driven facial reconstruction and animation methods.Comment: For project page, see https://sites.google.com/view/npfa/ Notice: You may not copy, reproduce, distribute, publish, display, perform, modify, create derivative works, transmit, or in any way exploit any such content, nor may you distribute any part of this content over any network, including a local area network, sell or offer it for sale, or use such content to construct any kind of databas

RELXILL_NK: a relativistic reflection model for testing Einstein's gravity

Einstein's theory of general relativity was proposed over 100 years ago and has successfully passed a large number of observational tests in the weak field regime. However, the strong field regime is largely unexplored, and there are many modified and alternative theories that have the same predictions as Einstein's gravity for weak fields and present deviations when gravity becomes strong. RELXILL_NK is the first relativistic reflection model for probing the spacetime metric in the vicinity of astrophysical black holes and testing Einstein's gravity in the strong field regime. Here we present our current constraints on possible deviations from Einstein's gravity obtained from the black holes in 1H0707-495, Ark 564, GX 339-4, and GS 1354-645.Comment: 8 pages, 6 figures. Talk given at the "International Conference on Quantum Gravity" (26-28 March 2018, Shenzhen, China). To appear in the conference proceeding