Zero-sum linear quadratic stochastic integral games and BSVIEs

This paper formulates and studies a linear quadratic (LQ for short) game problem governed by linear stochastic Volterra integral equation. Sufficient and necessary condition of the existence of saddle points for this problem are derived. As a consequence we solve the problems left by Chen and Yong in [3]. Firstly, in our framework, the term GX^2(T) is allowed to be appear in the cost functional and the coefficients are allowed to be random. Secondly we study the unique solvability for certain coupled forward-backward stochastic Volterra integral equations (FBSVIEs for short) involved in this game problem. To characterize the condition aforementioned explicitly, some other useful tools, such as backward stochastic Fredholm-Volterra integral equations (BSFVIEs for short) and stochastic Fredholm integral equations (FSVIEs for short) are introduced. Some relations between them are investigated. As a application, a linear quadratic stochastic differential game with finite delay in the state variable and control variables is studied.Comment: 27 page

Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations

Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs in short) are formulated and studied. A general duality principle is established for linear backward stochastic integral equation and linear stochastic Fredholm-Volterra integral equation with mean-field. With the help of such a duality principle, together with some other new delicate and subtle skills, Pontryagin type maximum principles are proved for two optimal control problems of FBSVIEs

John S. Service and United States-China relations, 1933--1945.

This dissertation examines John S. Service\u27s China career as a Foreign Service officer from 1933-45, and the impact of his diplomatic activities and political reports on Sino-American relations during World War II. It explores his dual heritage as an American missionary son who was born and bred in China, revealing how this American-Chinese experience affected his personality and diplomatic approach that proved to be critical in his distinctive life and career. World War II presented China and the United States with an unparalleled opportunity for close cooperation and the two countries worked to build an effective alliance, but the promising wartime cooperation soon deteriorated into disillusionment. The dramatic change in U.S.-China relations from friendly involvement to hostile non-recognition following the 1949 Communist victory triggered bitter debates in the United States over America\u27s China policy. Political analysts and historians have, for decades, posed questions as to how America lost China or suffered a lost chance in China. The focus of this political and scholarly scrutiny has been America\u27s wartime China policy and the role of such China hands as John Service. Despite the rich literature on Sino-American relations during World War II from both sides of the Pacific, the long posed question of whether America had adopted a realistic policy concerning wartime China needs to be clarified, and Service\u27s role in the dramatic Sino-American discourse fully investigated. The available literature on those subjects was largely written in the 1950s and 1960s during the Cold War, and in the 1970s amidst the China-mania. Moreover, they were mostly either based on fragmentary sources, chiefly in English, or influenced by political environment. The recent release of declassified archival material and primary documents in the United States and China makes it both possible and necessary to produce a more comprehensive and balanced study on Service and U.S.-China relations in the turbulent 1930s and 1940s. Based on extensive research on primary and secondary sources in English and Chinese, and on personal interviews with Service, this dissertation concludes that Service, with his extensive Chinese experience, was one of the few Americans who had a comprehensive understanding of China and its problems. His insights into Chinese political situations were firmly based; his prediction of a Chinese civil war and the Communist victory has withstood the test of time. His enthusiastic call for America\u27s assertive intervention in Chinese domestic affairs and his passionate effort to remake China along democratic lines, especially his recommendations of cooperating with the Chinese Communists were, despite his good intentions, impractical considering China\u27s strong nationalist sentiment and America\u27s long-standing anti-Communist politics. In the end America\u27s well-intentioned interventionist undertakings in China failed and Service, with his extraordinary career there, became a victim of history