A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page

S15RS SGR No. 5 (LSUPD Cameras)

A RESOLUTION To Urge and Request that the Louisiana State University Police Department reevaluate their amount and distribution of campus security camera

Using agronomic biofortification to boost zinc, selenium, and iodine concentrations of food crops grown on the loess plateau in China

Micronutrient malnutrition among humans is typically caused by micronutrient deficiency in soils and then staple food crops grown on these soils. In this study, field trials were conducted to investigate the biofortification of micronutrients in the edible parts of winter wheat, maize, soybean, potato, canola, and cabbage. Fertilizers of Se, Zn and I were applied to soil independently or together, while Se and Zn were sprayed as solution on winter wheat in another part of the trials. Selenium, when applied to the soil in the form of sodium selenate, whether alone or combined with Zn and⁄or I, was effective in increasing Se to around target levels in all of the tested crops. Selenium as sodium selenite was effective as a foliar application to winter wheat, increasing it from 25 to 312 µg kg⁻¹ in wheat grain with 60 g Se ha⁻¹ . For Zn, soil-applied zinc sulphate was only found to be effective for increasing the Zn concentration in cabbage leaf and canola seed, with 35 and 61 mg kg ⁻¹, respectively, while foliar zinc sulphate application was effective in biofortifying winter wheat, increasing grain Zn from 20 to 30 mg kg⁻¹ . While for I, soil-applied potassium iodate was only effective in increasing I concentration in cabbage leaf, and biofortification of the other crops was not possible. The enhancements of Se, Zn, and I concentration resulting from either the single or combined application of microelement fertilizers were similar. Therefore, agronomic biofortification of edible parts of various food crops with Zn, Se, and I can be an effective way to increase micronutrient concentrations, and the effectiveness depends on crop species, fertilizer forms and application methods.H. Mao, J. Wang, Z. Wang, Y. Zan, G. Lyons, C. Zo

Comparing Climate Change and Species Invasions as Drivers of Coldwater Fish Population Extirpations

Species are influenced by multiple environmental stressors acting simultaneously. Our objective was to compare the expected effects of climate change and invasion of non-indigenous rainbow smelt (Osmerus mordax) on cisco (Coregonus artedii) population extirpations at a regional level. We assembled a database of over 13,000 lakes in Wisconsin, USA, summarising fish occurrence, lake morphology, water chemistry, and climate. We used A1, A2, and B1 scenarios from the Intergovernmental Panel on Climate Change (IPCC) of future temperature conditions for 15 general circulation models in 2046–2065 and 2081–2100 totalling 78 projections. Logistic regression indicated that cisco tended to occur in cooler, larger, and deeper lakes. Depending upon the amount of warming, 25–70% of cisco populations are predicted to be extirpated by 2100. In addition, cisco are influenced by the invasion of rainbow smelt, which prey on young cisco. Projecting current estimates of rainbow smelt spread and impact into the future will result in the extirpation of about 1% of cisco populations by 2100 in Wisconsin. Overall, the effect of climate change is expected to overshadow that of species invasion as a driver of coldwater fish population extirpations. Our results highlight the potentially dominant role of climate change as a driver of biotic change

Evidence for Quasiparticle Decay in Photoemission from Underdoped Cuprates

I argue that the ``gap'' recently observed at the Brillouin zone face of cuprate superconductors in photoemission by Marshall et al [Phys. Rev. Lett. 76, 4841 (1996)] and Ding et al [Nature 382, 54 (1996)] is evidence for the decay of the injected hole into a spinon-holon pair.Comment: 4 pages of ReVTeX, 3 eps figure