In this paper it is demonstrated that the application of principal components analysis for regional cluster modelling and analysis is essential in the situations where there is significant multicollinearity among several parameters, especially when the dimensionality of regional data is measured in tens. The proposed principal components model allows for same-quality representation of the clustering of regions. In fact, the clusters become more distinctive and the apparent outliers become either more pronounced with the component model clustering or are alleviated with the respective hierarchical cluster. Thus, a five-component model was obtained and validated upon 85 regions of Russian Federation and 19 socio-economic parameters. The principal components allowed to describe approximately 75 percent of the initial parameters variation and enable further simulations upon the studied variables. The cluster analysis upon the principal components modelling enabled better exposure of regional structure and disparity in economic development in Russian Federation, consisting of four main clusters: the few-numbered highest development regions, the clusters with mid-to-high and low economic development, and the "poorest" regions. It is observable that the development in most regions relies upon resource economy, and the industrial potential as well as inter-regional infrastructural potential are not realized to their fullest, while only the wealthiest regions show highly developed economy, while the industry in other regions shows signs of stagnation which is scaled further due to the conditions entailed by economic sanctions and the recent Covid-19 pandemic. Most Russian regions are in need of additional public support and industrial development, as their capital assets potential is hampered and, while having sufficient labor resources, their donorship will increase.

Three radical ideas are presented. First, that justification for cancellation of principal is not justified in modern banking. Second, that non-cancellation of loan principal upon payment cures an old problem of maintenance of positive equity in the private sector. And third, that crediting this money to local government, creates an additional virtuous monetary circuit that ties finances of government directly to commercial activity.

This step can cure a problem I have identified with modern monetary theory, which is that breaking the monetary circuit of taxation in the minds of politicians will free them from centuries of restraint, optimizing their opportunities for implementing tyranny. It maintains and strengthens the current circuit, creating a new, more direct monetary circuit that does not enrich modern banks any more than they already are.

Bank's asset fire sales and recourse to central bank credit are modelled with continuous asset liquidity, allowing to derive the liability structure of a bank. Both asset sales liquidity and the central bank collateral framework are modeled as power functions within the unit interval. Funding stability is captured as a strategic bank run game in pure strategies between depositors. Fire sale liquidity and the central bank collateral framework determine jointly the ability of the banking system to deliver maturity transformation without endangering financial stability. The model also explains why banks tend to use the least liquid eligible collateral with the central bank and why a sudden non-anticipated reduction of asset liquidity, or a tightening of the collateral framework, can trigger a bank run. The model also shows that the collateral framework can be understood, beyond its aim to protect the central bank, as financial stability and non-conventional monetary policy instrument.

Stablecoins are one of the most widely capitalized type of cryptocurrency. However, their risks vary significantly according to their design and are often poorly understood. We seek to provide a sound foundation for stablecoin theory, with a risk-based functional characterization of the economic structure of stablecoins. First, we match existing economic models to the disparate set of custodial systems. Next, we characterize the unique risks that emerge in non-custodial stablecoins and develop a model framework that unifies existing models from economics and computer science. We further discuss how this modeling framework is applicable to a wide array of cryptoeconomic systems, including cross-chain protocols, collateralized lending, and decentralized exchanges. These unique risks yield unanswered research questions that will form the crux of research in decentralized finance going forward.

We introduce the notion of Worst-Case Sensitivity, defined as the worst-case rate of increase in the expected cost of a Distributionally Robust Optimization (DRO) model when the size of the uncertainty set vanishes. We show that worst-case sensitivity is a Generalized Measure of Deviation and that a large class of DRO models are essentially mean-(worst-case) sensitivity problems when uncertainty sets are small, unifying recent results on the relationship between DRO and regularized empirical optimization with worst-case sensitivity playing the role of the regularizer. More generally, DRO solutions can be sensitive to the family and size of the uncertainty set, and reflect the properties of its worst-case sensitivity. We derive closed-form expressions of worst-case sensitivity for well known uncertainty sets including smooth $\phi$-divergence, total variation, "budgeted" uncertainty sets, uncertainty sets corresponding to a convex combination of expected value and CVaR, and the Wasserstein metric. These can be used to select the uncertainty set and its size for a given application.