Probability Inequalities For ρ Mixing Sequence And The Estimating Of VaR

Probability theory is branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. limit theory is one of the key branches of Probability theory, and aslo the important foundation of other branches. The research purpose about recent Limit theory is to weaken the restrictions of inde-pendence and to customize them to reality for easier identification and application. As financial market develops, risk grows much more complicated. Risk is future’s uncertain loss, that is, volatility of the intending income. And risk can be caused by the volatility of both the unpredictable assets and the debt. How to measure the risk accurately is worthing of further research. Financial market risk is the most important one among all the risks. The emergence of Value at Risk (VaR) enables us to quantify the maximum loss of financial portfolios in certain period. And it has become the fundation of financial risk measurement system up to now.This thesis focuses mainly on probability inequalities for ρ mixing sequence and the estimating precision of VaR has to be improved.This thesis includes four parts.In the first part,we introduces background of limit theorem of random variable and the overview on the documents of VaR.In the second part,we study the moment inequality for ρ mixing sequence.By the moment inequality, we obtain the three series theorem for ρ mixing sequence.We aslo give some new results of probaility inequalities for ρ mixing sequence.In the third part the estimating methods of VaR were discussed. The definition and traditional estimating methods were summarized.In the forth part Bootstrap and random weighting methods were applied to es-timate VaR, which helped to get more accurate estimator of VaR.