Based on the work of Suzuki, we consider a generalization of Merton's asset valuation approach in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous asset values. In...

There exists a simple, didactically useful one-to-one relationship between stopping times and adapted càdlàg (RCLL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times. Furthermore, we show how minimal elements of a...

Based on the work of Suzuki (2002), we consider a generalization of Merton's asset valuation approach (Merton, 1974) in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous...

Much research in systemic risk is focused on default contagion. While this demands an understanding of valuation, fewer articles specifically deal with the existence, the uniqueness, and the computation of equilibrium prices in structural models of interconnected financial systems. However,...

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates...

For the convenience of readers of the article {\em No-arbitrage pricing under systemic risk: accounting for cross-ownership} (Fischer, 2012, arXiv:1005.0768), a full proof of Lemma A.5 and a shorter proof of Lemma A.6 of that paper are provided.

A simple quantitative example of a reflexive feedback process and the resulting price dynamics after an exogenous price shock to a financial network is presented. Furthermore, an outline of a theory that connects financial reflexivity, which stems from cross-ownership and delayed or incomplete...