Optimal Investment under Model Uncertainty

Start: 04/12/2012 - 4:30pm
End  : 04/12/2012 - 5:30pm

Statistics/OR/Math Finance Seminar

Scott Robertson (Carnegie Mellon University)


Realistic models for stock prices incorporate randomness in future movements. For example, in the binomial model, during each time period, the stock price goes either up or down, with the probability of an up movement given by some number p. Once p is fixed, the stock price, while still a random process, has a well defined model governing its dynamics. In this talk, we will consider the case when there is uncertainty in how to model the dynamics of the underlying asset. Specified to the binomial model, this means that we do not know p exactly, but rather that we know that p lies in some interval (a,b). In this environment, we wish to invest in a robust manner, so that we do relatively well in all possible models.  It will be shown that the existence of an optimal trading strategy, different from just putting all your money in your pocket and doing nothing, is intimately related to the "distance" between the risk-neutral model and the class of acceptable models. Time permitting, results will be extended to the Black-Scholes model in continuous time.


Third floor Sprague Library, Harvey Mudd College