King's College London

Landslides are generally associated with a trigger, such as an earthquake, a rapid snowmelt or a large storm. The trigger event can generate a single landslide or many thousands. This paper examines: (i) The frequency-area statistics of several triggered landslide event inventories, which are characterized by a three-parameter inverse-gamma probability distribution (exponential for small landslide areas, power-law for medium and large areas). (ii) The use of proxies (newspapers) for compiling long-time series of landslide activity in a given region, done in the context of the Emilia-Romagna region, northern Italy. (iii) A stochastic model developed to evaluate the probability of landslides intersecting a simple road network during a landslide triggering event.

We study portfolio optimization and contingent claim valuation in markets where illiquidity may affect the transfer of wealth over time and between investment classes. In addition to classical frictionless markets and markets with transaction costs, our model covers nonlinear illiquidity effects that arise in limit order markets. We extend basic results on arbitrage bounds, attainable claims and optimal portfolios to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of portfolio optimization under conditions that extend the no-arbitrage condition in the classical linear market model.

This talk surveys the well known relationship between half-flat SU(3) structures on 6-manifolds M and metrics with holonomy in G_2 on Mx(a,b), focusing on the case in which M=S3xS3 with solutions invariant by SO(4).

I will present a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. These loops are calculated on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. I will comment about the feasibility of deriving all-loop results for these Wilson loops.

Consistent truncations have proved to be powerful tools in the construction of new string theory solutions. Recently, they have been employed in the holographic description of condensed matter systems. In the talk, I will present a rich class of supersymmetric consistent truncations of higher-dimensional supergravity which are based on geometric structures, focusing on the tri-Sasakian case. Then I will discuss some applications, including a general result relating AdS backgrounds to solutions with non-relativistic Lifshitz symmetry.

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

We consider random walks on two classes of random graphs and explore the likely structure of the the set of unvisited vertices or vacant set. In both cases, the size of the vacant set $N(t)$ can be obtained explicitly as a function of $t$. Let $\Gamma(t)$ be the subgraph induced by the vacant set. We show that, for random graphs $G_{n,p}$ above the connectivity threshold, and for random regular graphs $G_r$, for constant $r\geq 3$, there is a phase transition in the sense of the well-known Erdos-Renyi phase transition. Thus for $t\leq (1-\epsilon)t^*$ we have a unique giant plus components of  size $O(\log n)$ and for $t\geq (1+\epsilon)t^*$ we have only components of  size $O(\log n)$.

In the case of $G_r$ we describe the likely degree sequence, size of the giant component and structure of the small ($O(\log n)$) size components.

We present three examples of credit products whose valuation poses challenging modeling problems related to armageddon scenarios and extreme losses, analyzing their behaviour pre- and in-crisis.

The products are Credit Index Options (CIOs), Collateralized Debt Obligations (CDOs), and Credit Valuation Adjustment (CVA) related products. We show that poor mathematical treatment of possibly vanishing numeraires in CIOs and lack of modes in the tail of the loss distribution in CDOs may lead to inaccurate valuation, both pre- and especially in crisis. We also consider the limits of copula models in trying to represent systemic risk in credit intensity models. We finally enlarge the picture and comment on a number of common biases in the public perception of modeling in relationship with the crisis.