arXiv subjects

Steffen Schuldenzucker

Publications and source records attributed to Steffen Schuldenzucker.

4 recordsLinked to original sources

arXiv2023

Equilibria and Convergence in Fire Sale Games

The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.

cs.GT↗

arXiv2022

Designing Autonomous Markets for Stablecoin Monetary Policy

We develop a new type of automated market maker (AMM) that helps to maintain stability and long-term viability in a stablecoin. This primary market AMM (P-AMM) is an autonomous mechanism for pricing minting and redemption of stablecoins in all possible states and is designed to achieve several desirable properties. We first cover several case studies of current ad hoc stablecoin issuance and redemption mechanisms, several of which have contributed to recent stablecoin de-peggings, and formulate desirable properties of a P-AMM that support stability and usability. We then design a P-AMM redemption curve and show that it satisfies these properties, including bounded loss for both the protocol and stablecoin holders. We further show that this redemption curve is path independent and has properties of path deficiency in extended settings involving trading fees and a separate minting curve. This means that system health weakly improves relative to the path independent setting along any trading curve and that there is no incentive to strategically subdivide redemptions. Finally, we show how to implement the P-AMM efficiently on-chain.

cs.CR↗

arXiv2019

Monotonic and Non-Monotonic Solution Concepts for Generalized Circuits

Generalized circuits are an important tool in the study of the computational complexity of equilibrium approximation problems. However, in this paper, we reveal that they have a conceptual flaw, namely that the solution concept is not monotonic. By this we mean that if $\varepsilon < \varepsilon'$, then an $\varepsilon$-approximate solution for a certain generalized circuit is not necessarily also an $\varepsilon'$-approximate solution. The reason for this non-monotonicity is the way Boolean operations are modeled. We illustrate that non-monotonicity creates subtle technical issues in prior work that require intricate additional arguments to circumvent. To eliminate this problem, we show that the Boolean gates are a redundant feature: one can simulate stronger, monotonic versions of the Boolean gates using the other gate types. Arguing at the level of these stronger Boolean gates eliminates all of the aforementioned issues in a natural way. We hope that our results will enable new studies of sub-classes of generalized circuits and enabler simpler and more natural reductions from generalized circuits to other equilibrium search problems.

cs.CC↗

arXiv2019

The Computational Complexity of Financial Networks with Credit Default Swaps

The 2008 financial crisis has been attributed to "excessive complexity" of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of clearing a financial network after a shock. Prior work has shown that when banks can only enter into simple debt contracts with each other, then this problem can be solved in polynomial time. In contrast, if they can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank, a solution may not even exist. In this work, we show that deciding if a solution exists is NP-complete if CDSs are allowed. This remains true if we relax the problem to $\varepsilon$-approximate solutions, for a constant $\varepsilon$. We further show that, under sufficient conditions where a solution is guaranteed to exist, the approximate search problem is PPAD-complete for constant $\varepsilon$. We then try to isolate the "origin" of the complexity. It turns out that already determining which banks default is hard. Further, we show that the complexity is not driven by the dependence of counterparties on each other, but rather hinges on the presence of so-called naked CDSs. If naked CDSs are not present, we receive a simple polynomial-time algorithm. Our results are of practical importance for regulators' stress tests and regulatory policy.

q-fin.RM↗