Peter Lee

First passage models, where corporate assets undergo a random walk and default occurs if the assets fall below a threshold, provide an attractive framework for modeling the default process. Recently such models have been generalized to allow a fluctuating default threshold or equivalently a fluctuating total recovery fraction $R$. For a given company a particular type of debt has a recovery fraction $R_i$ that is greater or less than $R$ depending on its level of subordination. In general the $R_i$ are functions of $R$ and since, in models with a fluctuating default threshold, the probability of default depends on $R$ there are correlations between the recovery fractions $R_i$ and the probability of default. We find, using a simple scenario where debt of type $i$ is subordinate to debt of type $i-1$, the functional dependence $R_i(R)$ and explore how correlations between the default probability and the recovery fractions $R_i(R)$ influence the par spreads for credit default swaps. This scenario captures the effect of debt cushion on recovery fractions.

We consider open strings ending on a D5-brane in the pp-wave background, which is realized in the Penrose limit of ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ with an ${\mathrm{AdS}}_4\times {\mathrm{S}}^2$ brane. A complete set of gauge invariant operators in the defect conformal field theory is constructed which is dual to the open-string states.

We use the supergravity modes to clarify the role of the prefactor in the light-cone superstring field theory on a pp-wave background. We verify some of the proposals of Constable et al. and give further evidence for the correspondence between $\mathcal{N}=4\mathrm{}$ Super Yang-Mills gauge theory and string theory on a pp-wave. We also consider energy-preserving processes and find that they give a vanishing cubic interaction Hamiltonian matrix.