Abstract
The paper concerns a piecewise linear process controlled by the set of velocities {cn}n≥0 consecutively switched after exponentially distributed, Exp(λn), n ≥ 0, time intervals. The distribution of such process is studied in detail, including the distribution of the first passage time through the constant boundary. The processes which moves by alternating patterns and with a double jump component are also studied
Highlights
A class of random processes with excitation at random times is studied for a long time in various aspects
The telegraph processes describing noninteracting particles, which move with finite constant velocities switchable over an exponentially distributed random time intervals have been studied by many authors beginning with Taylor (1922)
In this paper we study the continuous piecewise linear process L = L(t), t ≥ 0, L(t) =
Summary
A class of random processes with excitation at random times is studied for a long time in various aspects. In the context of market model based on Hawkes processes the optimal execution problem is solved explicitly by Alfonsi and Blanc (2016) This presentation continues the author’s paper Ratanov (2014), where the explicit formula for the moment generating function of the piecewise linear process L(t), t > 0, was given. This model involves switching tendencies (accompanied by jumps of random amplitude) due to the internal market forces (small investors). It turns out that a certain policy of the strategic investor could provoke arbitrage
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Latin American Journal of Probability and Mathematical Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
