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

Calorimetric Evidence of Strong-Coupling Multiband Superconductivity in Fe(Te0.57Se0.43) Single Crystal

We have investigated the specific heat of optimally-doped iron chalcogenide superconductor Fe(Te0.57Se0.43) with a high-quality single crystal sample. The electronic specific heat Ce of this sample has been successfully separated from the phonon contribution using the specific heat of a non-superconducting sample (Fe0.90Cu0.10)(Te0.57Se0.43) as a reference. The normal state Sommerfeld coefficient gamma_n of the superconducting sample is found to be ~ 26.6 mJ/mol K^2, indicating intermediate electronic correlation. The temperature dependence of Ce in the superconducting state can be best fitted using a double-gap model with 2Delta_s(0)/kBTc = 3.92 and 2Delta_l(0)/kBTc = 5.84. The large gap magnitudes derived from fitting, as well as the large specific heat jump of Delta_Ce(Tc)/gamma_n*Tc ~ 2.11, indicate strong-coupling superconductivity. Furthermore, the magnetic field dependence of specific heat shows strong evidence for multiband superconductivity

Neutrino fluence after r-process freeze-out and abundances of Te isotopes in presolar diamonds

Using the data of Richter et al. (1998) on Te isotopes in diamond grains from a meteorite, we derive bounds on the neutrino fluence and the decay timescale of the neutrino flux relevant for the supernova r-process. Our new bound on the neutrino fluence F after freeze-out of the r-process peak at mass number A = 130 is more stringent than the previous bound F < 0.045 (in units of 10**37 erg/cm**2) of Qian et al. (1997) and Haxton et al. (1997) if the neutrino flux decays on a timescale tau > 0.65 s. In particular, it requires that a fluence of F = 0.031 be provided by a neutrino flux with tau < 0.84 s. Such a fluence may be responsible for the production of the solar r-process abundances at A = 124-126 (Qian et al. 1997; Haxton et al. 1997). Our results are based on the assumption that only the stable nuclei implanted into the diamonds are retained while the radioactive ones are lost from the diamonds upon decay after implantation (Ott 1996). We consider that the nanodiamonds are condensed in an environment with C/O > 1 in the expanding supernova debris or from the exterior H envelope. The implantation of nuclei would have occurred 10**4-10**6 s after r-process freeze-out. This time interval may be marginally sufficient to permit adequate cooling upon expansion for the formation of diamond grains. The mechanisms of preferential retention/loss of the implanted nuclei are not well understood.Comment: AASTeX, 11 pages, 3 Postscript figure