A financial market with interacting investors: does an equilibrium exist?

While trading on a financial market, the agents we consider take the performance of their peers into account. By maximizing individual utility subject to investment constraints, the agents may ruin each other even unintentionally so that no equilibrium can exist. However, when the agents are willing to waive little expected utility, an approximated equilibrium can be established. The study of the associated backward stochastic differential equation (BSDE) reveals the mathematical reason for the absence of an equilibrium. Presenting an illustrative counterexample, we explain why such multidimensional quadratic BSDEs may not have solutions despite bounded terminal conditions and in contrast to the one-dimensional case.     

Does Bitcoin dominate the price discovery of the Cryptocurrencies market? A time-varying information share analysis

Using a time-varying vector error correction model (VECM), we examine the dynamic information shares of the top four Cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Ripple (XRP) and Litecoin (LTC) over 1/1/2016–31/12/2019. Although steadily decreasing, the information share of BTC is still the largest as of end-2019. The individual dominances of market capitalization and trading volume can explain 20% of variations of the BTC information share but only 6% of those for ETH.     

Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?

We study the complexity of scalar 2mth order elliptic two-point boundary-value problems Lu=f, error being measured in the energy norm. Previous work on the complexity of these problems has generally assumed that we had partial information about the right-hand side f and complete information about the coefficients of L. In this paper, we study the complexity of such problems when, in addition to partial information about f, we have only partial information about the coefficients of L. More precisely, we suppose that f has r derivatives in the L_p-sense, with r⩾−m and p∈[2, ∞], and that L has the usual divergence form Lv=∑_{0⩽i, j⩽m} (−1)ⁱ Dⁱ(a_i, j D^jv), with a_i, j being r_i, j-times continuously differentiable, where r_i, j⩾0. We first suppose that continuous linear information is available. Let r=min{r, min_{0⩽i, j⩽m} {r_i, j−i}}. If r=−m, the problem is unsolvable; for r>−m, we find that the ε-complexity is proportional to (1/ε)^1/(r+m), and we show that a finite element method (FEM) is optimal. We next suppose that only standard information (consisting of function and/or derivative evaluations) is available. Let r_min=min{r, min_{0⩽i, j⩽m} {r_i, j}}. If r_min=0, the problem is unsolvable; for r_min>0, we find that the ε-complexity is proportional to (1/ε)^1/r_min, and we show that a modified FEM (which uses only function evaluations, and not derivatives) is optimal.     

Is there chaos in the Spanish labour market?

One could argue that there is a resurgence of the non-linear modelling in economics. Some instruments have been developed to measure the complexity or instability of the analysed systems. At the present work some of these developed techniques are applied to verify the non-linearity present in the time series of Spanish unemployment, as well as to quantify the degree of complexity of the system that has generated the series. Using these techniques we find evidence of chaos in Spanish unemployment time series.     

The ‘invisible science’: operational research for the British Armed Forces after 1945

This paper presents an original account of the contribution of operational research (OR) to the formulation of tactics and strategy on behalf of the British Armed Forces in the four decades after 1945. The main focus is on the Cold War in the European theatre, where OR analysts devoted considerable time and effort to the modelling of warfare on behalf of the British Army of the Rhine. In the absence of combat data for nuclear weapons, OR analysts devised a sequence of war games which evolved in conformity with the development of NATO strategy in relation to the Warsaw Pact. Again in the context of the Cold War, the paper analyses the role of OR in relation to the early V bomber force and the introduction of ‘global war studies’ on behalf of the Royal Navy. The paper also comments on the organisational structure of British military OR following on the creation of a centralised OR facility within the Ministry of Defence in 1965. In conclusion, the paper notes the sea-change in military OR following the end of the Cold War in 1990 and the onset of a period of sustained ‘asymmetric’ military operations in the former Yugoslavia, the Middle East and Afghanistan.     

Limited time commitment: Does competition for providing scarce products always improve the supplies?

In addition to the fact that goods and services typically become scarce because resources are scarce, scarcity involves a psychological aspect. When a product is limited in availability, or perceived as being limited, it becomes more attractive. As a result, as long as the product is viewed as scarce, a surplus in supplies implies an increase in consumption. Motivated by fresh-water scarcity, we address the problem of dynamic interaction between two firms committing to provide water supply within a limited time horizon. We find that competition does not necessarily reduce product scarcity compared to the monopolistic industry. In particular, commitment-based market equilibrium is characterized by a critical duration of the supply contract. Duopolistic competition within this duration is reminiscent of the conventional quantity competition—the supply grows and the price drops compared to the monopolistic output. On the other hand, a longer contract leads to a different operational outcome—the monopoly becomes gradually more beneficial in terms of supplies and, as the time horizon grows, even overwhelmingly advantageous, thereby resulting in lower scarcity of the products.     

Does negative type characterize the round sphere?

We discuss the measure-theoretic metric invariants extent, mean distance and symmetry ratio and their relation to the concept of negative type of a metric space. A conjecture stating that a compact Riemannian manifold with symmetry ratio must be a round sphere was put forward by the author in 2004. We resolve this conjecture in the class of Riemannian symmetric spaces by showing that a Riemannian manifold with symmetry ratio must be of negative type and that the only compact Riemannian symmetric spaces of negative type are the round spheres.

     

Does the loss of regularity really appear?

In the theory of weakly hyperbolic equations we have the effect of loss of regularity. The present paper devotes to the study of two problems. On the one hand we describe families of weakly hyperbolic Cauchy problems for which we have no loss of regularity. On the other hand we discuss the question if the loss of derivatives really appears. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk setting. A Loss Distributional Approach (LDA) for modeling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of α-stable severities is considered. There has been little analysis of such models to date and it is believed insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies, the intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss processes and claims processes in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.     

Solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of weak solutions to a more general integro-differential equation by using the Schaefer’s fixed point theorem and generalize the result to unbounded domains.     

Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis

Current studies that use traditional data envelopment analysis (DEA) neglect the 100% market share restriction. This study adopts zero-sum gains data envelopment analysis to measure the efficiency scores of securities firms (SFs) and indicates that the traditional DEA model underestimates the efficiency scores of inefficient SFs. This research analyses 266 integrated securities firms in Taiwan from 2001 to 2005 and employs three inputs (fixed assets, financial capital, and general expenses) and a single output (market share). The foreign-affiliated ownership of SFs positively affects the efficiency scores. The two-stage least squares procedure confirms that the market share and efficiency score simultaneously reinforce each other.     

Solutions to a gradient-dependent integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of solutions in a general domain by proving a uniform bound on an iterative sequence of solutions and then applying the Arzelà–Ascoli theorem.     

Does the Balanced Scorecard make a difference to the strategy development process?

A great number of strategy tools are being taught in strategic management modules. These tools are available to managers for use in facilitating strategic decision making and enhancing the strategy development process in their organisations. A number of studies have been published examining which are the most popular tools; however there is little empirical evidence on how their utilisation influences the strategy process. This paper is based on a large scale international survey on the strategy development process, and seeks to examine the impact of a particular strategy tool, the Balanced Scorecard (BSC), upon the strategy process. Recently, it has been suggested that as a strategy tool, the BSC can influence all elements of the strategy process. The results of this study indicate that although there are significant differences in some elements of the strategy process between the organisations that have implemented the BSC and those that have not, the impact is not comprehensive.     

Effective formulas for the local ?ojasiewicz exponent

We give an effective formula for the local ?ojasiewicz exponent of a polynomial mapping. Moreover, we give an algorithm for computing the local dimension of an algebraic variety.     

Does the location and the institutional background matter in convergence modelling of the EU regions?

Central European Journal of Operations Research - The paper focuses on the testing of regional income convergence of NUTS2 EU regions during the 2000–2011 period with the emphasis on...     

Are there elimination algorithms for the permanent?

We define the class of elimination algorithms. There are algebraic algorithms for evaluating multivariate polynomials, and include as a special case Gaussian elimination for evaluating the determinant. We show how to find the linear symmetries of a polynomial, defined appropriately, and use these methods to find the linear symmetries of the permanent and determinant. We show that in contrast to the Gaussian elimination algorithm for the determinant, there is no elimination algorithm for the permanent.     

Does a population with the highest turnover coefficient win competition?

We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We give sufficient conditions for competitive exclusion and the existence of periodic solutions related to the classical logistic, Beverton–Holt and Ricker models.