機率研討會
主講者: 1.韓傳祥教授 (清華大學計量財務金融學系) 2.許順吉教授 (中央研究院數學研究所)
講題: 1.Estimation of Joint Default Probability by Efficient Importance sampling 2.HJB equations for the optimization of consumption and expected utility
時間: 2008-12-01 (Mon.)  14:00 - 17:00
地點:
Abstract: (1) Estimating joint default probabilities plays a central role in the evaluation of credit derivatives, and risk management of credit portfolio. Models of default based on intensity, copula and structure are considered. A generic importance sampling method is developed to estimate joint default probability with a moment analysis. By large deviation theory we prove that the importance sampling is indeed optimal. Under scenarios such as stochastic volatility and/or correlation, we consider the homogenization under large deviations. A variance analysis is discussed. In the end we present some applications in credit derivatives and risk management of credit portfolio. (2) The investment problems to optimize consumption and to optimize expected utility are considered. Using a factor model we show an interesting connection of these two problems. The solution of the Hamilton-Jacobi-Bellman(HJB) equation for the optimization of the expected utility is used to construct a supersolution of the HJB equation of optimal consumption problem. Hence the latter problem can be solved. This is a report of an on going project with Hiroaki Hata.
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