Semimartingales on rays, Walsh diffusions, and related problems of control and stopping

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Karatzas, Ioannis²  Yan, Minghan¹ 

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] Investment Management, One Palmer Sq,Suite 441, Princeton, NJ 08542 USA

关键词: Semimartingales on rays;    Tree-topology;    Walsh semimartingales and diffusions;    Skorokhod reflection;    Local time;    Stochastic calculus;    Explosion times;    Feller's test;    Stochastic control;    Optimal stopping;   

DOI  :  10.1016/j.spa.2018.06.012

来源: Elsevier

【 摘 要 】

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 processes are diffusions which choose, once at 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 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 stochastic control with discretionary stopping involving Walsh diffusions. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free