Agency problems with non-smooth decision profiles: the case of monopoly under product quality

A method for dealing with monotonicity constraints in optimal control problems is used to generalize some results in the context of monopoly theory, also extending the generalization to a large family of principal-agent programs. Our main conclusion is that many results on diverse economic topics, achieved under assumptions of continuity and piecewise differentiability in connection with the endogenous variables of the problem, still remain valid after replacing such assumptions by two minimal requirements.

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is specially suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Web didáctica para la aproximación de funciones mediante redes neuronales

In this article we presents a project [1] developed to demonstrate the capability that Multi-Layer Perceptrons (MLP) have to approximate non-linear functions [2]. The simulation has been implemented in Java to be used in all the computers by Internet [3], with a simple operation and pleasant interface. The power of the simulations is in the possibility of the user of seeing the evolutions of the approaches, the contribution of each neuron, the control of the different parameters, etc. In addition, to guide the user during the simulation, an online help has been implemented.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

The domain and interpretation of utility functions: An exploration

This paper proposes an exploration of the methodology of utilityfunctions that distinguishes interpretation from representation. Whilerepresentation univocally assigns numbers to the entities of the domainof utility functions, interpretation relates these entities withempirically observable objects of choice. This allows us to makeexplicit the standard interpretation of utility functions which assumesthat two objects have the same utility if and only if the individual isindifferent among them. We explore the underlying assumptions of suchan hypothesis and propose a non-standard interpretation according towhich objects of choice have a well-defined utility although individualsmay vary in the way they treat these objects in a specific context.We provide examples of such a methodological approach that may explainsome reversal of preferences and suggest possible mathematicalformulations for further research.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

Background: During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.

The promoter activity of human Mfn2 depends on Sp1 in vascular smooth muscle cells

AIMS: Mitofusin-2 (Mfn2) expression is dysregulated in vascular proliferative disorders and its overexpression attenuates the proliferation of vascular smooth muscle cells (VSMCs) and neointimal lesion development after balloon angioplasty. We sought to gain insight into the mechanisms that control Mfn2 expression in VSMCs. METHODS AND RESULTS: We cloned and characterized 2 kb of the 5'-flanking region of the human Mfn2 gene. Its TATA-less promoter contains a CpG island. In keeping with this, 5'-rapid amplification of cDNA ends revealed six transcriptional start sites (TSSs), of which TSS2 and TSS5 were the most frequently used. The strong CpG island was found to be non-methylated under conditions characterized by large differences in Mfn2 gene expression. The proximal Mfn2 promoter contains six putative Sp1 motifs. Sp1 binds to the Mfn2 promoter and its overexpression activates the Mfn2 promoter in VSMCs. Chemical inhibition of Sp1 reduced Mfn2 expression, and Sp1 silencing reduced transcriptional activity of the Mfn2 promoter. In keeping with this view, Sp1 and Mfn2 mRNA levels were down-regulated in the aorta early after an atherogenic diet in apolipoprotein E-knockout mice or in VSMCs cultured in the presence of low serum. CONCLUSION: Sp1 is a key factor in maintaining basal Mfn2 transcription in VSMCs. Given the anti-proliferative actions of Mfn2, Sp1-induced Mfn2 transcription may represent a mechanism for prevention of VSMC proliferation and neointimal lesion and development.

The promoter activity of human Mfn2 depends on Sp1 in vascular smooth muscle cells

AIMS: Mitofusin-2 (Mfn2) expression is dysregulated in vascular proliferative disorders and its overexpression attenuates the proliferation of vascular smooth muscle cells (VSMCs) and neointimal lesion development after balloon angioplasty. We sought to gain insight into the mechanisms that control Mfn2 expression in VSMCs. METHODS AND RESULTS: We cloned and characterized 2 kb of the 5'-flanking region of the human Mfn2 gene. Its TATA-less promoter contains a CpG island. In keeping with this, 5'-rapid amplification of cDNA ends revealed six transcriptional start sites (TSSs), of which TSS2 and TSS5 were the most frequently used. The strong CpG island was found to be non-methylated under conditions characterized by large differences in Mfn2 gene expression. The proximal Mfn2 promoter contains six putative Sp1 motifs. Sp1 binds to the Mfn2 promoter and its overexpression activates the Mfn2 promoter in VSMCs. Chemical inhibition of Sp1 reduced Mfn2 expression, and Sp1 silencing reduced transcriptional activity of the Mfn2 promoter. In keeping with this view, Sp1 and Mfn2 mRNA levels were down-regulated in the aorta early after an atherogenic diet in apolipoprotein E-knockout mice or in VSMCs cultured in the presence of low serum. CONCLUSION: Sp1 is a key factor in maintaining basal Mfn2 transcription in VSMCs. Given the anti-proliferative actions of Mfn2, Sp1-induced Mfn2 transcription may represent a mechanism for prevention of VSMC proliferation and neointimal lesion and development.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia