Mihail Zervos

Optimal Stopping of One-dimensional Diffusions with Generalised Drift

We consider the problem of optimally stopping a one-dimensional diffusion with generalised drift over an infinite horizon. We develop a complete characterisation of the problem's value function and optimal stopping strategy in terms of a variational inequality. We then solve the special case that arises when the state process is a skew geometric Brownian motion and the reward function is the one of financial call option. We show that the optimal stopping strategy can take several qualitatively different forms, depending on parameter values.

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