演講訊息 TALKS

摘要: In the study of optimal investment problem that we want to optimize the expected utility, martingale method and dynamic programming approach are frequently used. The martingale method is very useful when the market is complete. It can be applied to general utility functions. The dynamic programming approach can be used for Markovian (diffusion) model. Using this approach, the HJB (Hamilton-Jacobi-Bellman) equation can be derived. A candidate of optimal investment strategy can be obtained from a solution of HJB equation. I will use some examples to show these two ideas. I will also show a recent idea how these two approaches can be used together to derive an iteration procedure that we may solve the optimal investment problems for some Markovian incomplete market models. 參考：Karatzas and S.E. Shreve (1998) Methods of Mathematical Finance, 1998, Springer W.H. Fleming and S.J. Sheu (1999) Optimal Long Time Growth Rate of Expected Utility of Wealth, Ann. Appl. Probab. , 9, P871-903