FINTECH THRUST SEMINAR | Optimal Investment Stopping Problems with Partial Information
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Optimal Investment Stopping Problems with Partial Information
Abstract:
We study a finite-horizon optimal investment stopping problem with an unobservable random variable for the return of the risky asset. Using the Bayesian filter and the dual control approach, we transform the original primal problem into a dual finite horizon optimal stopping problem, which results in the dual value function satisfying a variational inequality with two state variables. For a class of utility functions that include power utility and non-HARA utility, we show that the free boundary satisfies a Volterra type nonlinear integral equation with expectation over the joint distribution of the dual state process and the filtered probability process and we simplify and solve the integral equation with the dimension reduction and backward recursive methods. We also construct two simple closed form approximations for the free boundary using its asymptotic properties and show their accuracy and efficiency with numerical examples. Furthermore, we demonstrate that different model parameters may lead to one, or two, or no free boundaries with a simple example. (Joint work with Jingtang Ma and Jie Xing)
Harry Zheng is a professor of mathematics at Imperial College. His main research is in stochastic control, dynamic portfolio optimization, and mathematical finance. His publications are mainly in operational research and financial mathematics journals (OR, MOR, MF, FS, SICON, Automatica, etc.). Prior to joining Imperial, he was a lecturer in the business school at the University of Edinburgh for several years. He did a BSc/MSc at Fudan University and a PhD at the University of British Columbia.