Optimal Dynamic Risk Sharing when Enforcement is a Decision Variable

Societies provide institutions that are costly to set up, but able to enforce long-run relationships. We study the optimal decision problem of using self-governance for risk sharing or governance through enforcement provided by these institutions. Third-party enforcement is modelled as a costly technology that consumes resources, but permits the punishment of agents who deviate from ex-ante specified allocations. We show that it is optimal to employ the technology whenever commitment problems prevent first-best risk sharing, but never optimal to provide incentives exclusively via this technology. Commitment problems then persist and the optimal incentive structure changes dynamically over time with third-party enforcement monotonically increasing in the relative inequality between agents.Limited Commitment, Risk Sharing, Third-party Enforcement

Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach. For instance, we exemplarily formulate and solve a marginal master equation describing the protein translation and degradation in a fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio

Moment-Based Variational Inference for Markov Jump Processes

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning (ICML 2019

How Flexible Can Inflation Targeting Be? Suggestions for the Future of Canada's Targeting Regime

In Canada, inflation targeting is widely agreed to have been a success story, but questions about how the regime might be fine-tuned in 2011 remain open. This Commentary asks how much discretion an inflation-targeting Bank of Canada can be allowed without compromising the credibility of its low inflation goal.monetary policy, Bank of Canada, inflation targeting

Optimal dynamic risk sharing when enforcement is a decision variable

JEL Classification: C73, D60, D91, K49dynamic risk sharing, enforcement

Central counterparties

Central counterparties (CCPs) have increasingly become a cornerstone of financial markets infrastructure. We present a model where trades are time-critical, liquidity is limited and there is limited enforcement of trades. We show a CCP novating trades implements efficient trading behaviour. It is optimal for the CCP to face default losses to achieve the efficient level of trade. To cover these losses, the CCP optimally uses margin calls, and, as the default problem becomes more severe, also requires default funds and then imposes position limits

A variational approach to path estimation and parameter inference of hidden diffusion processes

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing densities of the signal process. The paper then demonstrates how an efficient inference scheme, based on this variational approach to the approximation of the hidden states, can be designed to estimate the unknown parameters of stochastic differential equations. Two examples at the end illustrate the efficacy and the accuracy of the presented method.Comment: 37 pages, 2 figures, revise

The Emergence and Future of Central Counterparties

We study the role of a central counterparty (CCP) in controlling counterparty risk. When trading is organized via a centralized exchange with fungible contracts -- as in a futures market -- we show that it is optimal to clear trades via a CCP that uses (i) novation to pool the risk of default and (ii) mutualization of losses to insure against the aggregate cost of default in the form of price risk. We then analyze the design of CCP clearing for over-the-counter (OTC) trades where contracts are customized and, hence, not fungible. A CCP can still offer gains from novation by pooling default risk across all customized contracts. Bargaining in OTC trades leads to an inefficient allocation of default risk across trades. A transfer scheme can alleviate this inefficiency, but necessitates novation being offered by a CCP. Hence, the benefit from CCP clearing for OTC markets goes beyond simple netting as it is a prerequisite for an efficient allocation of default risk in such markets.Central Counterparty, Clearing, Over-the-counter Markets, Novation and Mutualization, Default Risk

The emergence and future of central counterparties

The authors explain why central counterparties (CCPs) emerged historically. With standardized contracts, it is optimal to insure counterparty risk by clearing those contracts through a CCP that uses novation and mutualization. As netting is not essential for these services, it does not explain why CCPs exist. In over-the-counter markets, as contracts are customized and not fungible, a CCP cannot fully guarantee contract performance. Still, a CCP can help: As bargaining leads to an inefficient allocation of default risk relative to the gains from customization, a transfer scheme is needed. A CCP can implement it by offering partial insurance for customized contracts.Risk management ; Over-the-counter markets ; Contracts

Evolution of Feedback Loops in Oscillatory Systems

Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved. Based on published models from the mitotic cycle in embryogenesis, we build a few case studies. Using a simple core architecture (transcription, phosphorylation and degradation), we define oscillatory models having either one positive feedback or one negative feedback, or both loops. With these models, we address the following questions about evolvability: could a system evolve from a simple model to a more complex one with a continuous transition in the parameter space? How do new feedback loops emerge without disrupting the proper function of the system? Our results show that progressive formation of a second feedback loop is possible without disturbing existing oscillatory behavior. For this process, the parameters of the system have to change during evolution to maintain predefined properties of oscillations like period and amplitude.Comment: Proceedings of the 2009 FOSBE conference in Denver, CO, USA. 4 page