2016/03/10 by Ioannis Karatzas, Karatzas, Ioannis, Minghan Yan +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1603.03124
We introduce a class of continuous planar processes, called "semimartingales on rays", and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such planar processes are diffusions which choose, once they reach the origin, the rays for their subsequent voyage according to a fixed probability measure in the manner of Walsh (1978). We develop existence and uniqueness results up to an explosion time for these "Walsh diffusions", study their asymptotic behavior, and develop tests for explosions in finite time. We use these results to find an optimal strategy, in a problem of control with discretionary stopping involving Walsh diffusions.