Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components.We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplementalmaterials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Health Programming for Clergy: An Overview of Protestant Programs in the United States

The health of clergy is important, and clergy may find health programming tailored to them more effective. Little is known about existing clergy health programs. We contacted Protestant denominational headquarters and searched academic databases and the Internet. We identified 56 clergy health programs and categorized them into prevention and personal enrichment; counseling; marriage and family enrichment; peer support; congregational health; congregational effectiveness; denominational enrichment; insurance/strategic pension plans; and referral-based programs. Only 13 of the programs engaged in outcomes evaluation. Using the Socioecological Framework, we found that many programs support individual-level and institutional-level changes, but few programs support congregational-level changes. Outcome evaluation strategies and a central repository for information on clergy health programs are needed. © 2011 Springer Science+Business Media, LLC.

Programming stress-induced altruistic death in engineered bacteria.

Programmed death is often associated with a bacterial stress response. This behavior appears paradoxical, as it offers no benefit to the individual. This paradox can be explained if the death is 'altruistic': the killing of some cells can benefit the survivors through release of 'public goods'. However, the conditions where bacterial programmed death becomes advantageous have not been unambiguously demonstrated experimentally. Here, we determined such conditions by engineering tunable, stress-induced altruistic death in the bacterium Escherichia coli. Using a mathematical model, we predicted the existence of an optimal programmed death rate that maximizes population growth under stress. We further predicted that altruistic death could generate the 'Eagle effect', a counter-intuitive phenomenon where bacteria appear to grow better when treated with higher antibiotic concentrations. In support of these modeling insights, we experimentally demonstrated both the optimality in programmed death rate and the Eagle effect using our engineered system. Our findings fill a critical conceptual gap in the analysis of the evolution of bacterial programmed death, and have implications for a design of antibiotic treatment.

Metabolic programming and PDHK1 control CD4+ T cell subsets and inflammation.

Activation of CD4+ T cells results in rapid proliferation and differentiation into effector and regulatory subsets. CD4+ effector T cell (Teff) (Th1 and Th17) and Treg subsets are metabolically distinct, yet the specific metabolic differences that modify T cell populations are uncertain. Here, we evaluated CD4+ T cell populations in murine models and determined that inflammatory Teffs maintain high expression of glycolytic genes and rely on high glycolytic rates, while Tregs are oxidative and require mitochondrial electron transport to proliferate, differentiate, and survive. Metabolic profiling revealed that pyruvate dehydrogenase (PDH) is a key bifurcation point between T cell glycolytic and oxidative metabolism. PDH function is inhibited by PDH kinases (PDHKs). PDHK1 was expressed in Th17 cells, but not Th1 cells, and at low levels in Tregs, and inhibition or knockdown of PDHK1 selectively suppressed Th17 cells and increased Tregs. This alteration in the CD4+ T cell populations was mediated in part through ROS, as N-acetyl cysteine (NAC) treatment restored Th17 cell generation. Moreover, inhibition of PDHK1 modulated immunity and protected animals against experimental autoimmune encephalomyelitis, decreasing Th17 cells and increasing Tregs. Together, these data show that CD4+ subsets utilize and require distinct metabolic programs that can be targeted to control specific T cell populations in autoimmune and inflammatory diseases.