Studies On A Class Of Optimal Investment Stopping Problems Under Inverse Completely Monotonic Utility In Finite Time

In this thesis,we study the optimal investment stopping problem between a single risky asset and a risk-free asset in a complete financial market.The utility function used in this thesis has the inverse completely monotonic feature,and this kind of utility function contains a wide class of utility functions often used in the optimal investment problem.We use the dynamic programming principle to transform the optimal investment stopping problem into HJB variational inequality.Then using the dual control method,a dual free boundary problem of a linear PDE is obtained.According to the property of completely monotonic function,we take the Taylor expansion of the inverse completely monotonic utility functions.According to the coefficient characteristics of Taylor's expansion,the dual free boundary problems are divided into three types: the case of no free boundary,the case of single free boundary and the case of multiple free boundaries.Moreover,the method for the nonexistence of free boundary and the condition for the existence of free boundary are given.We also study the monotonic properties and asymptotic properties for the free boundaries.Finally,according to the strong duality and the smooth pasting condition,the free boundary of the original optimal investment stopping problem is obtained.In the end,we use logarithmic utility function,exponential utility function and non hyperbolic absolute risk aversion(non-HARA)utility function to verify the theoretical results using binomial tree algorithms.