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
A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We ...A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.展开更多
By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integ...By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integrate each part by calculating its phase flow,and develop explicit symplectic integrators of different orders for the original Hamiltonian by composing the phase flows.A 2nd-order reversible constructed symplectic scheme is employed to simulate solitons motion and invariants behavior of the NLSE.The simulation results are compared with a 3rd-order non-symplectic implicit Runge-Kutta method,and the convergence of the formal energy of this symplectic integrator is also verified.The numerical results indicate that the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical tool for solving the NLSE.展开更多
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This research was partially supported by the Natural Science Research Foundation of Shaanxi Province(2001SL09)
文摘A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.
基金This research is partially supported by the Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences“Supercomputing En-vironment Construction and Application”(INF105-SCE)National Natural Science Foundation of China(Grant Nos.10471145 and 10672143).
文摘By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integrate each part by calculating its phase flow,and develop explicit symplectic integrators of different orders for the original Hamiltonian by composing the phase flows.A 2nd-order reversible constructed symplectic scheme is employed to simulate solitons motion and invariants behavior of the NLSE.The simulation results are compared with a 3rd-order non-symplectic implicit Runge-Kutta method,and the convergence of the formal energy of this symplectic integrator is also verified.The numerical results indicate that the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical tool for solving the NLSE.
