Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Electronic couplings and on-site energies for hole transfer in DNA: systematic quantum mechanical/molecular dynamic study

The electron hole transfer (HT) properties of DNA are substantially affected by thermal fluctuations of the π stack structure. Depending on the mutual position of neighboring nucleobases, electronic coupling V may change by several orders of magnitude. In the present paper, we report the results of systematic QM/molecular dynamic (MD) calculations of the electronic couplings and on-site energies for the hole transfer. Based on 15 ns MD trajectories for several DNA oligomers, we calculate the average coupling squares 〈 V2 〉 and the energies of basepair triplets X G+ Y and X A+ Y, where X, Y=G, A, T, and C. For each of the 32 systems, 15 000 conformations separated by 1 ps are considered. The three-state generalized Mulliken-Hush method is used to derive electronic couplings for HT between neighboring basepairs. The adiabatic energies and dipole moment matrix elements are computed within the INDO/S method. We compare the rms values of V with the couplings estimated for the idealized B -DNA structure and show that in several important cases the couplings calculated for the idealized B -DNA structure are considerably underestimated. The rms values for intrastrand couplings G-G, A-A, G-A, and A-G are found to be similar, ∼0.07 eV, while the interstrand couplings are quite different. The energies of hole states G+ and A+ in the stack depend on the nature of the neighboring pairs. The X G+ Y are by 0.5 eV more stable than X A+ Y. The thermal fluctuations of the DNA structure facilitate the HT process from guanine to adenine. The tabulated couplings and on-site energies can be used as reference parameters in theoretical and computational studies of HT processes in DNA

Multiuser detection in a dynamic environment — Part II: Joint user identification and parameter estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We doso deriving Bayesian recursions that describe the evolution withtime of a posteriori densities of the unknown parameters and data.Unlike in the above cited paper, wherein one could evaluate theexact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximationsfor the receivers that are based on Sequential Monte Carlo (SMC)methods (“particle filtering”). Simulation results, referring to acode-divisin multiple-access (CDMA) system, are presented toillustrate the theory.

Large-system analysis of a CDMA dynamic channel under a Markovian input process

We study the minimum mean square error (MMSE) and the multiuser efficiency η of large dynamic multiple access communication systems in which optimal multiuser detection is performed at the receiver as the number and the identities of active users is allowed to change at each transmission time. The system dynamics are ruled by a Markov model describing the evolution of the channel occupancy and a large-system analysis is performed when the number of observations grow large. Starting on the equivalent scalar channel and the fixed-point equation tying multiuser efficiency and MMSE, we extend it to the case of a dynamic channel, and derive lower and upper bounds for the MMSE (and, thus, for η as well) holding true in the limit of large signal–to–noise ratios and increasingly large observation time T.

A dynamic choice model of hybrid behavior in the attribute-space

This paper presents a dynamic choice model in the attributespace considering rational consumers that discount the future. In lightof the evidence of several state-dependence patterns, the model isfurther extended by considering a utility function that allows for thedifferent types of behavior described in the literature: pure inertia,pure variety seeking and hybrid. The model presents a stationaryconsumption pattern that can be inertial, where the consumer only buysone product, or a variety-seeking one, where the consumer buys severalproducts simultane-ously. Under the inverted-U marginal utilityassumption, the consumer behaves inertial among the existing brands forseveral periods, and eventually, once the stationary levels areapproached, the consumer turns to a variety-seeking behavior. An empiricalanalysis is run using a scanner database for fabric softener andsignificant evidence of hybrid behavior for most attributes is found,which supports the functional form considered in the theory.

A positive theory of geographic mobility and social insurance

This paper presents a tractable dynamic general equilibrium model thatcan explain cross-country empirical regularities in geographical mobility,unemployment and labor market institutions. Rational agents vote overunemployment insurance (UI), taking the dynamic distortionary effects ofinsurance on the performance of the labor market into consideration.Agents with higher cost of moving, i.e., more attached to their currentlocation, prefer more generous UI. The key assumption is that an agent'sattachment to a location increases the longer she has resided there. UIreduces the incentive for labor mobility and increases, therefore, thefraction of attached agents and the political support for UI. The mainresult is that this self-reinforcing mechanism can give rise to multiplesteady-states-one 'European' steady-state featuring high unemployment,low geographical mobility and high unemployment insurance, and one'American' steady-state featuring low unemployment, high mobility andlow unemployment insurance.

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Towards a theory of the credit-risk balance sheet

This article designs what it calls a Credit-Risk Balance Sheet (the risk being that of default by customers), a tool which, in principle, can contribute to revealing, controlling and managing the bad debt risk arising from a company¿s commercial credit, whose amount can represent a significant proportion of both its current and total assets.To construct it, we start from the duality observed in any credit transaction of this nature, whose basic identity can be summed up as Credit = Risk. ¿Credit¿ is granted by a company to its customer, and can be ranked by quality (we suggest the credit scoring system) and ¿risk¿ can either be assumed (interiorised) by the company itself or transferred to third parties (exteriorised).What provides the approach that leads to us being able to talk with confidence of a real Credit-Risk Balance Sheet with its methodological robustness is that the dual vision of the credit transaction is not, as we demonstrate, merely a classificatory duality (a double risk-credit classification of reality) but rather a true causal relationship, that is, a risk-credit causal duality.Once said Credit-Risk Balance Sheet (which bears a certain structural similarity with the classic net asset balance sheet) has been built, and its methodological coherence demonstrated, its properties ¿static and dynamic¿ are studied.Analysis of the temporal evolution of the Credit-Risk Balance Sheet and of its applications will be the object of subsequent works.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Relevance of dynamic wetting in viscous fingering patterns

We demonstrate that wetting effects at moving contact lines have a strong impact in viscous fingering patterns. Experiments in a rotating Hele-Shaw (HS) cell, dry or prewetted, show consistent morphological differences. When the wetting fluid invades a dry region, contact angle dynamics yield a kinetic contribution to the interface pressure drop that scales with capillary number as Ca2¿3 but is significantly larger than the Park-Homsy kinetic correction. Numerical results are in very good agreement with experiments and show that standard HS equations work best for prewetted cells.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.