National attaches＇ great importance to price trends highlights the complexity of the situation of the current price. Control price at a reasonable level has become a large problem of the ＂The Twelfth Five-Year Guide...National attaches＇ great importance to price trends highlights the complexity of the situation of the current price. Control price at a reasonable level has become a large problem of the ＂The Twelfth Five-Year Guideline＂ for the first year of a major exam in front of us. At the end of Last year, the central economic work conference held to stabilize the overall price level in a more prominent position. The State Council raised that to ensure the overall price level basically stable on the first place in the deployment of the first quarter.展开更多
This paper deals with a constrained stochastic linear-quadratic（LQ for short）optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random c...This paper deals with a constrained stochastic linear-quadratic（LQ for short）optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Ito-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations（BSDEs for short）. The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.展开更多
文摘National attaches＇ great importance to price trends highlights the complexity of the situation of the current price. Control price at a reasonable level has become a large problem of the ＂The Twelfth Five-Year Guideline＂ for the first year of a major exam in front of us. At the end of Last year, the central economic work conference held to stabilize the overall price level in a more prominent position. The State Council raised that to ensure the overall price level basically stable on the first place in the deployment of the first quarter.
基金supported by the National Natural Science Foundation of China(Nos.10325101,11171076)the Shanghai Outstanding Academic Leaders Plan(No.14XD1400400)
文摘This paper deals with a constrained stochastic linear-quadratic（LQ for short）optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Ito-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations（BSDEs for short）. The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.
