Silvia Dedu

Quantitative Techniques for Financial Risk Assessment: A Comparative Approach Using Different Risk Measures and Estimation Methods

Abstract The aim of this paper is to highlight and illustrate the use of some quantitative techniques for risk estimation in finance and insurance. The first component involved in risk assessment concerns the risk measure used and the second one is based on the estimation technique. We will study the theoretical properties, the accuracy of modeling the economic phenomena and the computational performances of the risk measures Value-at-Risk, Conditional Tail Expectation, Conditional Value-at-Risk and Limited Value-at-Risk in the case of logistic distribution. We also investigate the most important statistical estimation methods for risk measure evaluation and we will compare their theoretical and empirical behavior. The quality of the risk estimation process corresponding to the quantitative techniques discussed will be tested for both real and simulated data. Numerical results will be provided.

A new approach in multi-objective portfolio optimization using Value-at-Risk based risk measure

Mean-risk models have been widely used in solving portfolio selection problems in the last years. Since the mean-variance theory of Markowitz, an enormous amount of papers have been published extending or modifying the basic model in several directions like the simplification of the type and amount of input data, the introduction of alternative measures of risk, the incorporation of additional criteria or constraints. Recently, risk measures concerned with the left tails of distributions that evaluate the extremely unfavourable outcomes are used. The most used risk measure for such purposes is Value-at-Risk (VaR). In this paper we concentrate on the second direction of incorporating of a new risk measure in portfolio modeling. We define a new risk measure, which take into consideration the values exceeding a certain threshold in the extreme tail of the loss distribution, called Limited Value-at-Risk (LVaR). We study the properties of this risk measure. We build a new model for portfolio selection, named mean-LVaR model, in which risk is evaluated using LVaR risk measure. We study the properties of the new mean-risk model and compare it with the classical mean-VaR model. We derive the analytical form of LVaR risk measure in the case of normal distribution. We provide computational results and analyze the implications of using the mean-LVaR risk model in portfolio optimization problem.

Entropy Measures for Assessing Volatile Markets

Abstract The application of entropy in finance can be regarded as the extension of information entropy and probability theory. In this article we apply the concept of entropy for underlying financial markets to make a comparison between volatile markets. We consider in the first step Shannon entropy with different estimators, Tsallis entropy for different values of its parameter, Renyi entropy and finally the approximate entropy. We provide computational results for these entropies for weekly and monthly data in the case of four different stock indices.

Multiobjective Mean-Risk Models for Optimization in Finance and Insurance

Abstract In this paper we propose some models for solving optimization problems which arise in finance and insurance. First the general framework for Mean-Risk models is introduced. Then several approaches for multiobjective programming, such as Mean-Value-at-Risk and Mean-Conditional Value-at-Risk are used for building the model Mean-Value-at-Risk-Conditional Value-at-Risk using both Value-at-Risk and Conditional Value-at-Risk simultaneously for risk assessment. A two stage portfolio optimization model is developed, using Value-at-Risk and also Conditional Value-at-Risk measures in two stages separately.

Modeling Financial Data Using Risk Measures with Interval Analysis Approach

Abstract In this paper we construct some new measures which can be used for risk assessment and optimization. Due to the random character of economic phenomena, modeling financial data by real numbers does not perform accurately in decision making problems under uncertainty. First we introduce some concepts related to interval analysis, by replacing real numbers with interval numbers. Using these concepts, some risk measures are defined in this new framework. The theoretical results obtained are used to solve a case study. Computational results are provided.

An Integrated Risk Measure and Information Theory Approach for Modeling Financial Data and Solving Decision Making Problems

Abstract In this paper we build some integrated techniques for modeling financial data and solving decision making problems, based on risk theory and information theory. Several risk measures and entropy measures are investigated and compared with respect to their analytical properties and effectiveness in solving real problems. Some criteria for portfolio selection are derived combining the classical risk measure approach with the information theory approach. We analyze the performance of the methods proposed in case of some financial applications.Computational results are provided.

Tsallis and Kaniadakis Entropy Measures for Risk Neutral Densities.

Concepts of Econophysics are usually used to solve problems related to uncertainty and nonlinear dynamics. The risk neutral probabilities play an important role in the theory of option pricing. The application of entropy in finance can be regarded as the extension of both information entropy and probability entropy. It can be an important tool in various financial issues such as risk measures, portfolio selection, option pricing and asset pricing. The classical approach of stock option pricing is based on Black-Scholes model, which relies on some restricted assumptions and contradicts with modern research in financial literature. The Black-Scholes model is governed by Geometric Brownian Motion and is based on stochastic calculus. It depends on two factors: no arbitrage, which implies the universe of risk-neutral probabilities and parameterization of risk-neutral probability by a reasonable stochastic process. Therefore, risk-neutral probabilities are vital in this framework. The Entropy Pricing Theory founded by Gulko represents an alternative approach of constructing risk-neutral probabilities without depending on stochastic calculus. Gulko applied Entropy Pricing Theory for pricing stock options and introduced an alternative framework of Black-Scholes model for pricing European stock options. In this paper we derive solutions of maximum entropy problems based on Tsallis, Weighted-Tsallis, Kaniadakis and Weighted-Kaniadakies entropies, in order to obtain risk-neutral densities.

Reflecting on Romanian Universities Ranking: An Entropy-Based Approach to Evaluate Scientific Research

Quantitative evaluation of scientific research activity involves a set of complex methodological aspects, many of which have not received so far the deserved attention, neither in theoretical, nor in empirical studies. The concept of entropy is widely used in decision-making problems as a useful instrument for assessing the amount and effect of information provided by certain criteria used to construct a composite indicator. This paper proposes the use of entropy to evaluate scientific research performance of academic units. The field of observation consists of Romanian universities classified either as Advanced Research and Education or Education and Scientific Research units, by national ranking exercise in 2011. Our analysis considers only ISI publications - Articles and Proceedings Papers, during 2006–2010. We argue that the evaluation of scientific research can be better addressed and these preliminary results on university rankings could be further validated when alternative methods of assessment are applied.