Dynamic Weighted Expected Shortfall And Its Application In The Portfolio

Financial risk runs through the whole process of financial market entities engaged in financial activities.Because there's a lot of uncertainty about the earnings and losses of the financial markets participants caused by financial risks,and it is difficult to accurately estimate the extent of the damage and the scope of impact from financial risks,the research on risk measurement is of great practical significance which is always regarded as a crucial step for investors to control and manage financial risks.In this paper,we divide the investment period and propose a new dynamic risk measurement-the dynamic weighted expected shortfall(DWES)based on the static risk measurement-weighted expected shortfall(WES),which extends the results in[10]from exponential weighted function to general nonlinear weighted function and greatly enriches existing risk measurement methods.This paper is divided into five parts.First of all,in the first chapter,the relevant research background and research status of financial risk measurement are described.In chapter 2,we first give some basic mathematical definitions and then briefly outline the common risk measures,such as value at Risk VaR?coherent risk measurement?ex-pected shortfall ES and weighted expected shortfall WES,where the weighted expected shortfall WES is proposed by introduceing a nonlinear weighted function based on the expected shortfall ES and different weights are assigned to different loss values,then we demonstrate that WES is more effective than ES in describe different investors' risk aversion level through actual stock data.Secondly,in chapter 3,we first introduce the definition of dynamic weighted expected shortfall(DWES),then we prove its convex-ity and monotonicity that a reasonable risk measure should have and other properties.After that,we discuss the choice of nonlinear weighted function w(x),and specify the selection of weighted functions and the range of parameters according to several com-mon loss distributions,which provides a theoretical basis for the practical application of DWES.Finally,chapter 4 and chapter 5 focus on the application of dynamic weighted expected shortfall(DWES)in the portfolio and the corresponding conclusion.We cal-culate and compare the static risk WES and dynamic risk DWES of portfolio investment in the same five periods in the case of different nonlinear weighted functions w(x),and we conclude as follows:the dynamic risk DWES in the current period is closely related to the earlier information and will have a lasting effect on the future risk fluctuation;In addition,for the fixed parameter,dynamic risk DWES under different forms of weighted function depict the risk differently,so we can measure the risk by choosing different nonlinear weighting function w(x)for investors with different risk appetite levels.