(2003). Risk Management: Value at Risk and Beyond. Journal of the American Statistical Association: Vol. 98, No. 462, pp. 494-494.

Risk Management: Value at Risk and Beyond

We assess the empirical importance of changes in income and relative prices for structural transformation in the postwar United States. We explain two natural approaches to the data: sectors may be categories of final expenditure or value added; e.g., the service sector may be the final expenditure on services or the value added from service industries. We estimate preferences for each approach and find that with final expenditure income effects are the dominant force behind structural transformation, whereas with value-added categories price effects are more important. We show how the inputoutput structure of the United States can reconcile these findings. (JEL E21, L16)

/pdf/two-perspectives-on-preferences-and-structural-1ioaefbfsr.pdf

Two perspectives on preferences and structural transformation

/pdf/mathematics-without-numbers-an-introduction-to-the-study-of-1sqsjd3myn.pdf

Mathematics without numbers: an introduction to the study of logic

We study the problem of sharing the revenue from broadcasting sport events, among participating players. We provide direct, axiomatic and game-theoretical foundations for two focal rules: the equal-split rule and concede-and-divide. The former allocates the revenues generated from broadcasting each game equally among the participating players in the game. The latter concedes players in each game the revenues generated by their respective fans and divides equally the residual. We also provide an application studying the case of sharing the revenue from broadcasting games in La Liga, the Spanish Football League. We show that hybrid schemes, combining our rules with lower bounds and performance measures, yield close outcomes to the current allocation being implemented by the Spanish National Professional Football League Association.

/pdf/sharing-the-revenues-from-broadcasting-sport-events-5ef02j9s4p.pdf

Sharing the Revenues from Broadcasting Sport Events

I feel that PR could best be achieved by allowing MPs to job share.
Put simply the percentage of the hours worked by each MP should

On Proportional Representation

Measuring and allocating risk properly are crucial for performance evaluation and internal capital allocation of portfolios held by banks, insurance companies, investment funds and other entities subject to financial risk. We show that by using a coherent measure of risk it is impossible to allocate risk satisfying the natural requirements of (Solution) Core Compatibility, Equal Treatment Property and Strong Monotonicity. To obtain the result we characterize the Shapley value on the class of totally balanced games and also on the class of exact games.

https://mpra.ub.uni-muenchen.de/26515/1/AixomShapley10.pdf

On the Impossibility of Fair Risk Allocation

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure.

/pdf/decentralized-clearing-in-financial-networks-1nmr7uvndi.pdf

Decentralized clearing in financial networks

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents’ assets might be insufficient to satisfy their liabilities, leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Since clearing payment matrices and the corresponding values of equity are not uniquely determined, we provide bounds on the possible levels equity can take. Unlike the existing literature, which studies centralized clearing procedures, we introduce a large class of decentralized clearing processes. We show the convergence of any such process in finitely many iterations to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing proce...

/pdf/decentralized-clearing-in-financial-networks-521o477cgt.pdf

Decentralized Clearing in Financial Networks

http://econ.core.hu/esemeny/korosi/2007/CSOKA07.PDF

Stable allocations of risk

Coherent measures of risk defined by the axioms of monotonicity, subadditivity, positive homogeneity, and translation invariance are recent tools in risk management to assess the amount of risk agents are exposed to. If they also satisfy law invariance and comonotonic additivity, then we get a subclass of them: spectral measures of risk. Expected shortfall is a well-known spectral measure of risk. We investigate the above mentioned six axioms using tools from general equilibrium (GE) theory. Coherent and spectral measures of risk are compared to the natural measure of risk derived from an exchange economy model, which we call the GE measure of risk. We prove that GE measures of risk are coherent measures of risk. We also show that spectral measures of risk are GE measures of risk only under stringent conditions, since spectral measures of risk do not take the regulated entity’s relation to the market portfolio into account. To give more insights, we characterize the set of GE measures of risk via the pricing kernel property.

/pdf/coherent-measures-of-risk-from-a-general-equilibrium-4kzb4phjn4.pdf

Péter Csóka

Papers

On the Impossibility of Fair Risk Allocation

Decentralized clearing in financial networks

Decentralized Clearing in Financial Networks

Stable allocations of risk

Coherent measures of risk from a general equilibrium perspective