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.

[1]  Silvia Dedu,et al.  Building an optimal portfolio using a mean-VaR framework , 2011 .

[2]  C. Tudor.  Active Portfolio Management on the Romanian Stock Market , 2012 .

[3]  George Georgescu,et al.  Public debt, Sovereign Risk and Sustainable Development of Romania , 2013 .

[4]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[5]  D. Năstac,et al.  A Neuro-Classification Model for Socio-Technical Systems , 2009 .

[6]  M. P. Biswal,et al.  Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables , 2012, Adv. Oper. Res..

[7]  G. P. Liu,et al.  A nonlinear interval number programming method for uncertain optimization problems , 2008, Eur. J. Oper. Res..

[8]  C. Tudor,et al.  On the Causal Relationship between Stock Returns and Exchange Rates Changes for 13 Developed and Emerging Markets , 2012 .

[9]  Istudor Ion,et al.  The Innovator Role of Technologies in Waste Management towards the Sustainable Development , 2014 .

[10]  Talla Nobibon,et al.  FOUNDATION AND FORMULATION OF STOCHASTIC INTERVAL PROGRAMMING , 2006 .

[11]  R. Lupu,et al.  Direction of change at the Bucharest Stock Exchange , 2008 .

[12]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[13]  Włodzimierz Ogryczak,et al.  Multiple criteria optimization and decisions under risk , 2002 .

[14]  Aida Toma,et al.  Quantitative Techniques for Financial Risk Assessment: A Comparative Approach Using Different Risk Measures and Estimation Methods☆ , 2014 .

[15]  Vasile Preda,et al.  Interval-Valued Optimization Problems Involving (α, ρ)-Right Upper-Dini-Derivative Functions , 2014, TheScientificWorldJournal.

[16]  Florin G. Filip.  A Decision-Making Perspective for Designing and Building Information Systems , 2012, Int. J. Comput. Commun. Control.

[17]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .