Bayesian sequential testing for Lévy processes with diffusion and jump components

Buonaguidi, Bruno; Muliere, Pietro

doi:10.1080/17442508.2016.1197926

“…These results follow previously obtained unpublished ones by Boyarchenko [3]. Similar type of techniques were applied in Buonaguidi and Muliere [4] to solve a statistical problem: the Bayesian sequential testing of two simple hypothesis. More recently, De Donno et al [7] found disconnected continuation regions in American put options with negative discount rates in Lévy models.…”

Section: Introductionsupporting

confidence: 85%

Two-sided optimal stopping for Lévy processes

Mordecki

¹

,

Oliú

²

2021

Electron. Commun. Probab.

View full text Add to dashboard Cite

Infinite horizon optimal stopping problems for a Lévy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A result to compute the angle of the value function at the optimal thresholds of the stopping region is given. To illustrate the results, the optimal stopping problem of a compound Poisson process with two-sided exponential jumps and a two-sided payoff function is solved. In this example, the smooth-pasting condition does not hold.

show abstract

“…These results follow previously obtained unpublished ones by Boyarchenko (2006). Similar type of techniques were applied in Buonaguidi and Muliere (2016) to solve a statistical problem: the Bayesian sequential testing of two simple hypothesis. More recently, De Donno et al (2019) found disconnected continuation regions in American put options with negative discount rates in Lévy models.…”

Section: Introductionsupporting

confidence: 85%

Two-sided optimal stopping for Lévy processes

Mordecki¹,

Oliú²

2019

Preprint

0

View full text Add to dashboard Cite

Infinite horizon optimal stopping problems for a Lévy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A result to compute the angle of the value function at the optimal thresholds of the stopping region is given. To illustrate the results, the optimal stopping problem of a compound Poisson process with two-sided exponential jumps and a two-sided payoff function is solved. In this example, the smooth-pasting condition does not hold.

show abstract