We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events accounting for correlations between the default events and...

In this work, we identify the most general measure of arbitrage for any market model governed by Ito processes. We show that our arbitrage measure is invariant under changes of numeraire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection....

A framework which consistently and fully integrates market, credit and country transfer risks of a general portfolio of financial assets in a multi-period setup is developed. An appropriate definition of exposure, loss-given-defaults and loss-given-transfer-events provides a unified treatment of...

We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected...

We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the...

Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose...