Evolutionary estimation of a Coupled Markov Chain credit risk model

There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this extent, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management

Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, the lowest upper bound on costs). However, hedging against an unlikely worst case may lead to losses in other situations. In general, one is interested in policies that behave well in all situations which results in a multi-objective view on decision making. In this paper, we consider policies for the expected discounted reward measure of MDPs with uncertain parameters. In particular, the approach is defined for bounded-parameter MDPs (BMDPs) [8]. In this setting the worst, best and average case performances of a policy are analyzed simultaneously, which yields a multi-scenario multi-objective optimization problem. The paper presents and evaluates approaches to compute the pure Pareto optimal policies in the value vector space.Comment: 9 pages, 5 figures, preprint for VALUETOOLS 201

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

Stochastic Optimization in Econometric Models – A Comparison of GA, SA and RSG

This paper shows that, in case of an econometric model with a high sensitivity to data, using stochastic optimization algorithms is better than using classical gradient techniques. In addition, we showed that the Repetitive Stochastic Guesstimation (RSG) algorithm –invented by Charemza-is closer to Simulated Annealing (SA) than to Genetic Algorithms (GAs), so we produced hybrids between RSG and SA to study their joint behavior. The evaluation of all algorithms involved was performed on a short form of the Romanian macro model, derived from Dobrescu (1996). The subject of optimization was the model’s solution, as function of the initial values (in the first stage) and of the objective functions (in the second stage). We proved that a priori information help “elitist “ algorithms (like RSG and SA) to obtain best results; on the other hand, when one has equal believe concerning the choice among different objective functions, GA gives a straight answer. Analyzing the average related bias of the model’s solution proved the efficiency of the stochastic optimization methods presented.underground economy, Laffer curve, informal activity, fiscal policy, transitionmacroeconomic model, stochastic optimization, evolutionary algorithms, Repetitive Stochastic Guesstimation

The Efficacy of Choosing Strategy with General Regression Neural Network on Evolutionary Markov Games

Nowadays, Evolutionary Game Theory which studies the learning model of players,has attracted more attention than before. These Games can simulate the real situationand dynamic during processing time. This paper creates the Evolutionary MarkovGames, which maps players’ strategy-choosing to a Markov Decision Processes(MDPs) with payoffs. Boltzmann distribution is used for transition probability andthe General Regression Neural Network (GRNN) simulating the strategy-choosing inEvolutionary Markov Games. Prisoner’s dilemma is a problem that uses the methodand output results showing the overlapping the human strategy-choosing line andGRNN strategy-choosing line after 48 iterations, and they choose the same strate-gies. Also, the error rate of the GRNN training by Tit for Tat (TFT) strategy is lowerthan similar work and shows a better re

The Spatial Agent-based Competition Model (SpAbCoM)

The paper presents a detailed documentation of the underlying concepts and methods of the Spatial Agent-based Competition Model (SpAbCoM). For instance, SpAbCoM is used to study firms' choices of spatial pricing policy (GRAUBNER et al., 2011a) or pricing and location under a framework of multi-firm spatial competition and two-dimensional markets (GRAUBNER et al., 2011b). While the simulation model is briefly introduced by means of relevant examples within the corresponding papers, the present paper serves two objectives. First, it presents a detailed discussion of the computational concepts that are used, particularly with respect to genetic algorithms (GAs). Second, it documents SpAbCoM and provides an overview of the structure of the simulation model and its dynamics. -- Das vorliegende Papier dokumentiert die zugrundeliegenden Konzepte und Methoden des Räumlichen Agenten-basierten Wettbewerbsmodells (Spatial Agent-based Competition Model) SpAbCoM. Anwendungsbeispiele dieses Simulationsmodells untersuchen die Entscheidung bezüglich der räumlichen Preisstrategie von Unternehmen (GRAUBNER et al., 2011a) oder Preissetzung und Standortwahl im Rahmen eines räumlichen Wettbewerbsmodells, welches mehr als einen Wettbewerber und zweidimensionalen Marktgebiete berücksichtigt. Während das Simulationsmodell in den jeweiligen Arbeiten kurz anhand eines Beispiels eingeführt wird, dient das vorliegende Papier zwei Zielen. Zum Einen sollen die verwendeten computergestützten Konzepte, hier speziell Genetische Algorithmen (GA), detailliert vorgestellt werden. Zum Anderen besteht die Absicht dieser Dokumentation darin, einen Überblick über die Struktur von SpAbCoM und die während einer Simulation ablaufenden Prozesse zu gegeben.Agent-based modelling,genetic algorithms,spatial pricing,location model.,Agent-basierte Modellierung,Genetische Algorithmen,räumliche Preissetzung,Standortmodell.

The Desirable Organizational Structure for Evolutionary Firms in Static Landscapes

In addition to the common analysis of the Kauffman NK model where the value of K and the structure of interaction is given, the aim of this paper is to study what would be the values of these two parameters if they were endogenized. Thus, a model is proposed where firms and business schools coordinate to search for high peaks in their respective landscapes using evolutionary algorithms. The main result coming out from the analysis of the model is that agents, using evolutionary algorithms, attempt to simplify the problems of coordination and this, over time, produces the existence in the economy of agents using many different strategies. (JEL-code: C61, C63, D21, D23