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Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function. 

Abstract We develop a convex‐optimization clustering algorithm for heterogeneous financial networks, in the presence of arbitrary or even adversarial outliers. In the stochastic block model with heterogeneity parameters, we penalize nodes whose degree exhibit unusual behavior beyond inlier heterogeneity. We prove that under mild conditions, this method achieves exact recovery of the underlying clusters. In absence of any assumption on outliers, they are shown not to hinder the clustering of the inliers. We test the performance of the algorithm on semi‐synthetic heterogenous networks reconstructed to match aggregate data on the Korean financial sector. Our method allows for recovery of sub‐sectors with significantly lower error rates compared to existing algorithms. For overlapping portfolio networks, we uncover a clustering structure supporting diversification effects in investment management. 

We introduce threshold growth in the classical threshold contagion model, or equivalently a network of Cramér-Lundberg processes in which nodes have downward jumps when there is a failure of a neighboring node. Choosing the configuration model as underlying graph, we prove fluid limits for the baseline model, as well as extensions to the directed case, state-dependent interarrival times and the case of growth driven by upward jumps. We obtain explicit ruin probabilities for the nodes according to their characteristics: initial threshold and in- (and out-) degree. We then allow nodes to choose their connectivity by trading off link benefits and contagion risk. We define a rational equilibrium concept in which nodes choose their connectivity according to an expected failure probability of any given link and then impose condition that the expected failure probability coincides with the actual failure probability under the optimal connectivity. We show existence of an asymptotic equilibrium and convergence of the sequence of equilibria on the finite networks. In particular, our results show that systems with higher overall growth may have higher failure probability in equilibrium.