A Nonlinear Optimal stopping problem

Specialeforsvar ved Peter Kruse Steinaa

Titel: A nonlinear Optimal Stopping problem

Abstrakt: Assuming that the stock price process is a geometric Brownian motion, this thesis analyses the optimal stopping problem for an investor who owns a stock and wishes to maximize his expected return while minimizing his risk upon selling the stock at time t. Inspired by the mean-variance analysis by Markowitz, we seek to find the optimal stopping time for selling the stock under a general p-moment risk measure. By applying the method of Lagrange multipliers we reduce the nonlinear problem to a family of linear problems. Solving the latter for choices of 1<p≤2 we derive a single barrier solution, that is consistent with the mean-variance analysis done by J. L. Pedersen & G. Peskir (2012) for p=2. For choices of p>2 the solution to the optimal stopping problem is given by a first exit time from an interval [a(x),b(x)], where a(x) and b(x) are the solutions to two equations

Vejleder: Jesper Lund Pedersen
Censor:    Claus Munk, CBS