Second Order Backward Stochastic Differential Equations with Quadratic Growth

We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$ variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.Comment: 31 page

Second order reflected backward stochastic differential equations

In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower c\`adl\`ag obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedging price for American options in a market with volatility uncertainty.Comment: Published in at http://dx.doi.org/10.1214/12-AAP906 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1003.6053 by other author

Integrated stakeholder analysis for effective urban flood management in a medium-sized city in China: a case study of Zhuji, Zhejiang province

Over recent decades, the stakeholder arena for urban flood management has become well recognised as being complex and dynamic. Various stakeholders are involved before, during and after a flooding event, all of which have different interests and demands. Therefore, an initial stakeholder identification and analysis stage is required before detailed stakeholder engagement strategies can be developed and employed. Drawing on urban flood management in Zhuji, a typical medium-sized city that has suffered urban flooding in China, this research project used a mixed-method research methodology within a single case-study approach to explore the current stakeholder arena for urban flood management in a medium-sized Chinese city. By combining stakeholder salience analysis with social network analysis, this study tries to create a more nuanced insight into the stakeholder arena, so that stakeholder participation in urban flood management can be improved. This thesis produces several findings. First, it provides empirical evidence to show that traditional one-dimensional stakeholder analysis methods such as the level of interest and influence; cooperation and competition; cooperation and threat; and stakeholder interest and power cannot provide an in-depth understanding of a complex and dynamic stakeholder arena, as exists for urban flood management. By way of contrast, the proposed stakeholder analysis approach, which combines both stakeholder salience and network analyses, can create a multi-dimensional understanding of urban flood management stakeholders and allows the initial problem space to be recast into a more detailed or nuanced understanding of the problems presented. This improved understanding of the stakeholder arena and the related problem space provides a more solid information foundation upon which new stakeholder and community engagement practices can be developed. Second, this thesis argues that the Mitchell et al. (1997) salience model experiences limitations in practice. Only five of the seven salience groups were identified in the present research project, with both the Dangerous and Demanding stakeholder groups missing. This indicates that the identification of urban flood management stakeholders in a medium-sized Chinese city is highly dependent on their legitimate claims. Third, the social network analysis used in this project not only explores the relationships between stakeholders, but also provides an opportunity to present other one-dimensional stakeholder attitudes. This enhancement of the data beyond one-dimensional visual representations to dynamic and interactive processes not only better assists policy-makers in developing new and improved engagement practices, it also allows engagement practitioners to educate stakeholders and interactively improve understanding of the situation among those stakeholders. This understanding, in turn, is assumed to facilitate collaborative problem solving

Structural characterization of the D290V mutation site in hnRNPA2 low-complexity-domain polymers.

Human genetic studies have given evidence of familial, disease-causing mutations in the analogous amino acid residue shared by three related RNA binding proteins causative of three neurological diseases. Alteration of aspartic acid residue 290 of hnRNPA2 to valine is believed to predispose patients to multisystem proteinopathy. Mutation of aspartic acid 262 of hnRNPA1 to either valine or asparagine has been linked to either amyotrophic lateral sclerosis or multisystem proteinopathy. Mutation of aspartic acid 378 of hnRNPDL to either asparagine or histidine has been associated with limb girdle muscular dystrophy. All three of these aspartic acid residues map to evolutionarily conserved regions of low-complexity (LC) sequence that may function in states of either intrinsic disorder or labile self-association. Here, we present a combination of solid-state NMR spectroscopy with segmental isotope labeling and electron microscopy on the LC domain of the hnRNPA2 protein. We show that, for both the wild-type protein and the aspartic acid 290-to-valine mutant, labile polymers are formed in which the LC domain associates into an in-register cross-β conformation. Aspartic acid 290 is shown to be charged at physiological pH and immobilized within the polymer core. Polymers of the aspartic acid 290-to-valine mutant are thermodynamically more stable than wild-type polymers. These observations give evidence that removal of destabilizing electrostatic interactions may be responsible for the increased propensity of the mutated LC domains to self-associate in disease-causing conformations

Second-order BSDEs with jumps: Formulation and uniqueness

In this paper, we define a notion of second-order backward stochastic differential equations with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190]. However, on the contrary to their formulation, where they can define pathwise the density of quadratic variation of the canonical process, in our setting, the compensator of the jump measure associated to the jumps of the canonical process, which is the counterpart of the density in the continuous case, depends on the underlying probability measures. Then in our formulation of 2BSDEJs, the generator of the 2BSDEJs depends also on the underlying probability measures through the compensator. But the solution to the 2BSDEJs can still be defined universally. Moreover, we obtain a representation of the $Y$ component of a solution of a 2BSDEJ as a supremum of solutions of standard backward SDEs with jumps, which ensures the uniqueness of the solution.Comment: Published at http://dx.doi.org/10.1214/14-AAP1063 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quadratic BSDEs with jumps: a fixed-point approach

In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z,u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.Comment: 29 page