In financial analysis risk quantification is essential for efficient portfolio management in a stochastic framework. In this paper we study the value at risk, the expected shortfall, marginal expected shortfall and va...In financial analysis risk quantification is essential for efficient portfolio management in a stochastic framework. In this paper we study the value at risk, the expected shortfall, marginal expected shortfall and value at risk, incremental value at risk and expected shortfall, the marginal and discrete marginal contributions of a portfolio. Each asset in the portfolio is characterized by a trend, a volatility and a price following a three-dimensional diffusion process. The interest rate of each asset evolves according to the Hull and White model. Furthermore, we propose the optimization of this portfolio according to the value at risk model.展开更多
In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper ...In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.展开更多
Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentration is on recent develo...Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentration is on recent developments in the estimation of the most popular risk measures, namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling. Then, parametric and nonparametric estimations of tail dependence are investigated. Finally, we conclude with insights into future research directions.展开更多
文摘In financial analysis risk quantification is essential for efficient portfolio management in a stochastic framework. In this paper we study the value at risk, the expected shortfall, marginal expected shortfall and value at risk, incremental value at risk and expected shortfall, the marginal and discrete marginal contributions of a portfolio. Each asset in the portfolio is characterized by a trend, a volatility and a price following a three-dimensional diffusion process. The interest rate of each asset evolves according to the Hull and White model. Furthermore, we propose the optimization of this portfolio according to the value at risk model.
基金Supported by the NNSF of China (10571141) the Key Project of the NNSF of China (70531030).
文摘In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.
基金the financial support,in part,from the National Science Fund of China(NSFC)for Distinguished Young Scholars(71625001)NSFC grant(71631004)(Key Project)the scholarship from China Scholarship Council(CSC)under the Grant CSC(N201706310023)
文摘Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentration is on recent developments in the estimation of the most popular risk measures, namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling. Then, parametric and nonparametric estimations of tail dependence are investigated. Finally, we conclude with insights into future research directions.
