In this paper, tile authors first study two kinds of stochastic differential equations （SDEs） with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimen...In this paper, tile authors first study two kinds of stochastic differential equations （SDEs） with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations （BSDEs） driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic （LQ） optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.展开更多
In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma ...In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.展开更多
基金This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814904the Natural Science Foundation of China under Grant No. 10671112+1 种基金Shandong Province under Grant No. Z2006A01Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20060422018
文摘In this paper, tile authors first study two kinds of stochastic differential equations （SDEs） with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations （BSDEs） driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic （LQ） optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.
基金supported by National Natural Science Foundation of China(Grant No.71271042)the Plan of Jiangsu Specially-Appointed Professors,the Jiangsu Hi-Level Innovative and Entrepreneurship Talent Introduction Plan and Major Program of Key Research Center in Financial Risk Management of Jiangsu Universities Philosophy Social Sciences(Grant No.2012JDXM009)
文摘In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.
