【中国精算研究院精算论坛】Tak Kuen Siu ：Functional Ito's Calculus and Dynamic Convex Risk Measures for Deri发布日期：2019-09-12 21:08:38
演讲题目：Functional Ito's Calculus and Dynamic Convex Risk Measures for Derivative
摘要：Using the functional Ito's calculus and forward-backward stochastic differential equations (FBSDEs), a new approach for evaluating dynamic convex risk measures for European-style derivative securities is proposed in a general, continuous-time financial market. The proposed approach can accommodate non-Markovian price processes of underlying risky assets. It consists of two stages. Initially, a dynamic convex risk measure for an unhedged position of derivative securities is represented as the conditional g-expectation which is given by the solution of the backward system in a FBSDE. Then, at the second stage, we use the functional Ito's calculus, a martingale representation and the unique decomposition of special semimartingales to identify the solution of the backward system in the FBSDE. In particular, the control component in the backward system is identified using functional derivatives. Whereas the first component of the backward system satisfies a functional partial differential equation.
演讲人：Tak Kuen Siu is an Associate Professor in Actuarial Studies at Macquarie University. His research areas are mathematical finance, actuarial science, risk management, stochastic calculus, filtering and control. He has published more than 100 research articles. Many have been published in top-tier international peer-reviewed journals such as SIAM Journal on Control and Optimization, Journal of Economic Dynamics and Control, ASTIN Bulletin, North American Actuarial Journal, Insurance Mathematics and Economics, Scandinavian Actuarial Journal, IEEE Transactions on Automatic Control, Automatica and Quantitative Finance. He was awarded the North American Actuarial Journal Annual Best Paper Award by the Society of Actuaries in the United States for his 2008 paper co-authored with Christian Erlwein and Rogemar Mamon. He is on the editorial boards of several journals, including Stochastics, IMA Journal of Management Mathematics and Annals of Financial Economics. He is a reviewer of Mathematical Reviews for American Mathematical Society and the Zentralblatt MATH of the European Mathematical Society. He serves as a reviewer for more than 40 international journals in various fields including actuarial science, economics, finance, statistics and applied mathematics.