Credit risk premia and quadratic BSDEs with a single jump

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Automated recognition of sunspots on the SOHO/MDI white light solar images

A new technique is presented for automatic identification of sunspots on the full disk solar images allowing robust detection of sunspots on images obtained from space and ground observations, which may be distorted by weather conditions and instrumental artefacts. The technique applies image cleaning procedures for elimination of limb darkening, intensity noise and noncircular image shape. Sobel edge-detection is applied to find sunspot candidates. Morphological operations are then used to filter out noise and define a local neighbourhood background via thresholding, with threshold levels defined as a function of the quiet sun intensity and local statistical properties. The technique was tested on one year (2002) of full disk SOHO/MDI white light (WL) images. The detection results are in very good agreement with the Mendon manual synoptic maps as well as with the Locarno Observatory Sunspot manual drawings. The detection results from WL observations are cross-referenced with the SOHO/MDI magnetogram data for verification purposes

Cross hedging with stochastic correlation

Cross hedging, Incomplete markets, Correlation, Local risk minimisation, BSDE, 91G20, 60H10, 60H07, C30, G13,