51 citations · 84 across the 12 of their papers we have counts for
12 papers
Consistency between transitive relations and between cones
Tom Fischer
A relation extends another relation consistently if its symmetric, respectively its asymmetric, part contains the corresponding part of the smaller relation. It is shown that there…
Share at least half the numbers in a nontrivial LCM-closed set a nontrivial divisor?
Tom Fischer
For a finite set of non-zero natural numbers that contains at least one element different from 1 and the least common multiple of any of its subsets, there exists a subset of at le…
No-Arbitrage Prices of Cash Flows and Forward Contracts as Choquet Representations
Tom Fischer
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is s…
Valuation Algorithms for Structural Models of Financial Interconnectedness
Johannes Hain, Tom Fischer
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 uniquenes…
A primer on reflexivity and price dynamics under systemic risk
Tom Fischer
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 o…
Cross-Ownership as a Structural Explanation for Over- and Underestimation of Default Probability
Sabine Karl, Tom Fischer
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…
Existence, uniqueness, and minimality of the Jordan measure decomposition
Tom Fischer
This is a note of purely didactical purpose as the proof of the Jordan measure decomposition is often omitted in the related literature. Elementary proofs are provided for the exis…
A shorter proof of Lemma A.6 (arXiv:1005.0768)
Tom Fischer
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…
Minimal elements of stopping time -algebras
Tom Fischer
We show how minimal elements of a stopping time -algebra can be expressed in terms of the minimal elements of the -algebra of the underlying filtration. This facilitates an i…
Stopping times are hitting times: a natural representation
Tom Fischer
There exists a simple, didactically useful one-to-one relationship between stopping times and adapted càglàd (LCRL) processes that are non-increasing and take the values 0 and 1 on…
No-arbitrage pricing under cross-ownership
Tom Fischer
We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may incl…
Consumption processes and positively homogeneous projection properties
Tom Fischer
We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (…