2020
DOI: 10.1137/19m1305355
|View full text |Cite
|
Sign up to set email alerts
|

Long-Run Risk-Sensitive Impulse Control

Abstract: In this paper, we investigate the effects of applying generalised (non-exponential) discounting on a long-run impulse control problem for a Feller-Markov process. We show that the optimal value of the discounted problem is the same as the optimal value of its undiscounted version. Next, we prove that an optimal strategy for the undiscounted discrete time functional is also optimal for the discrete-time discounted criterion and nearly optimal for the continuous-time discounted one. This shows that the discounte… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
5
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
6
3

Relationship

3
6

Authors

Journals

citations
Cited by 13 publications
(5 citation statements)
references
References 44 publications
0
5
0
Order By: Relevance
“…where the second inequality follows from (29), the third inequality from log E[ f (s) + ḡ(s)] ≥ E( f (s)) + E(ḡ(s)), the fourth inequality from Jensen's inequality, and the last one from Assumption 1. By changing the roles of Q π 1 k with Q π 2 k we obtain (18). This completes the proof.…”
Section: Appendix a Proof Of Proposition 1 Considermentioning
confidence: 53%
“…where the second inequality follows from (29), the third inequality from log E[ f (s) + ḡ(s)] ≥ E( f (s)) + E(ḡ(s)), the fourth inequality from Jensen's inequality, and the last one from Assumption 1. By changing the roles of Q π 1 k with Q π 2 k we obtain (18). This completes the proof.…”
Section: Appendix a Proof Of Proposition 1 Considermentioning
confidence: 53%
“…This paper extends the results from [17], where the function G is assumed to be bounded. In that case, it can be shown that the Bellman equation admits a unique solution, which can be used to prove continuity of the function u ≡ w. This result was one of the main building blocks used in [16], where the long-run impulse control problem was analysed. In the present paper we show a more general sufficient condition for the identity u ≡ w. This may be used to generalise the results from [16] to the unbounded case.…”
Section: Introductionmentioning
confidence: 98%
“…This paper extends the results from Jelito et al (2021), where the function G is assumed to be bounded. In that case, it can be shown that Bellman equation admits a unique solution, which can be used to prove continuity of the function u ≡ w. This result was one of the main building blocks used in Jelito et al (2020), where the long-run impulse control problem was analysed. In the present paper we show a more general sufficient condition for the identity u ≡ w. This may be used to generalise the results from Jelito et al (2020) to the unbounded case.…”
Section: Introductionmentioning
confidence: 98%