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A Course In Functional Analysis

: Scientific learning is an iterative process employing Criticism and Estimation. Correspondingly the formulated model factors into two complimentary parts - a predictive part allowing model criticism, and a Bayes posterior part allowing estimation. Implications for significance tests, the theory of precise measurement, and for ridge estimates are considered. Predictive checking functions for transformation, serial correlation, bad values, and their relation with Bayesian options are considered. Robustness is seen from a Bayesian viewpoint and examples are given. For the bad value problem a comparison with M estimators is made. (Author)

Sampling and Bayes' inference in scientific modelling and robustness

This paper presents the result of a field experiment on the effectiveness of non-monetary incentives on pupils' achievement on a mathematical multiple choice test. Our sample consists of 2113 pupils of deprived and high-achieving secondary schools in Germany. Based on a pre-study, we compare the effectiveness of (i) a medal (ii) a letter of praise to the parents and (iii) a delegation of choice over incentives. The effect of non-monetary incentives depends on pupils' socio-economic background. While they constitute a potentially cost-effective and easily implementable method of motivation in Non-High Schools, predetermined non-monetary incentives crowd out intrinsic motivation for pupils in High Schools. In contrast, the endogenous choice of the reward increases pupils' willingness to prepare for the test and mitigates the negative effect of predetermined external rewards in High Schools. Additionally, in the delegation treatment, we find that low-achieving pupils typically choose a reward with a higher signaling value to their parents, independent of the school type.

https://www.econstor.eu/bitstream/10419/122939/1/840595662.pdf

Peers or parents? On non-monetary incentives in schools

We introduce a network valuation model (hereafter NEVA) for the ex-ante valuation of claims among financial institutions connected in a network of liabilities. Similar to previous work, the new framework allows to endogenously determine the recovery rate on all claims upon the default of some institutions. In addition, it also allows to account for ex-ante uncertainty on the asset values, in particular the one arising when the valuation is carried out at some time before the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution.

/pdf/network-valuation-in-financial-systems-53xtyh23t9.pdf

Network Valuation in Financial Systems

The field of Financial Networks is a paramount example of the novel applications of Statistical Physics that have made possible by the present data revolution. As the total value of the global financial market has vastly outgrown the value of the real economy, financial institutions on this planet have created a web of interactions whose size and topology calls for a quantitative analysis by means of Complex Networks. Financial Networks are not only a playground for the use of basic tools of statistical physics as ensemble representation and entropy maximization; rather, their particular dynamics and evolution triggered theoretical advancements as the definition of DebtRank to measure the impact and diffusion of shocks in the whole systems. In this review we present the state of the art in this field, starting from the different definitions of financial networks (based either on loans, on assets ownership, on contracts involving several parties -- such as credit default swaps, to multiplex representation when firms are introduced in the game and a link with real economy is drawn) and then discussing the various dynamics of financial contagion as well as applications in financial network inference and validation. We believe that this analysis is particularly timely since financial stability as well as recent innovations in climate finance, once properly analysed and understood in terms of complex network theory, can play a pivotal role in the transformation of our society towards a more sustainable world.

The Physics of Financial Networks

In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics of the interbank liabilities. Emphasis will be placed on the construction, existence, and uniqueness of the continuous-time framework and its formulation as a differential equation driven by the operating cash flows. Finally, the financial implications of time dynamics will be considered. The focus will be on how the dynamic clearing solutions differ from those of the static Eisenberg-Noe model.

Dynamic Clearing and Contagion in Financial Networks

In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with bankruptcy costs. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios so as to provide analytical stress testing formulas. We endogenously construct the comonotonic endowment setting from a equity maximizing standpoint with capital transfers. We conclude by, numerically, comparing the network valuation problem with two single firm baseline heuristics which can, respectively, approximate the price of debt and equity.

Pricing of debt and equity in a financial network with comonotonic endowments

In this paper we apply the gravity model to the panel consisting of India’s yearly bilateral trade data with all its trading partners in the second half of the twentieth century. The main conclusions that emerge from our analyses are: (1) The core gravity model can explain around 43 per cent of the fluctuations in India’s direction of trade in the second half of the twentieth century (2) India’s trade responds less than proportionally to size and more than proportionally to distance (3) Colonial heritage is still an important factor in determining India’s direction of trade at least in the second half of the twentieth century (4) India trades more with developed rather than underdeveloped countries, however (5) size has more determining influence on India’s trade than the level of development of the trading partner.

/pdf/does-the-gravity-model-explain-india-s-direction-of-trade-a-4c5ox5enwg.pdf

Does the Gravity Model Explain India's Direction of Trade? A Panel Data Approach

Price mediated contagion through capital ratio requirements with VWAP liquidation prices

In this paper we study the implications of contingent payments on the clearing wealth in a network model of financial contagion. We consider an extension of the Eisenberg–Noe financial contagion model in which the nominal interbank obligations depend on the wealth of the firms in the network. We first consider the problem in a static framework and develop conditions for existence and uniqueness of solutions as long as no firm is speculating on the failure of other firms. In order to achieve existence and uniqueness under more general conditions, we introduce a dynamic framework. We demonstrate how this dynamic framework can be applied to problems that were ill-defined in the static framework.

Tathagata Banerjee

Papers

Dynamic Clearing and Contagion in Financial Networks

Pricing of debt and equity in a financial network with comonotonic endowments

Does the Gravity Model Explain India's Direction of Trade? A Panel Data Approach

Price mediated contagion through capital ratio requirements with VWAP liquidation prices

Impact of contingent payments on systemic risk in financial networks