scholarly journals Impulse control and expected suprema

2017 ◽  
Vol 49 (1) ◽  
pp. 238-257 ◽  
Author(s):  
Sören Christensen ◽  
Paavo Salminen
Keyword(s):  
Nonlinear Equation ◽  
Markov Processes ◽  
Real Line ◽  
Impulse Control ◽  
Control Problems ◽  
Main Ingredient ◽  
Excessive Functions ◽  
Representation Result ◽  
Optimal Impulse ◽  
Strong Markov

Abstract We consider a class of impulse control problems for general underlying strong Markov processes on the real line, which allows for an explicit solution. The optimal impulse times are shown to be of a threshold type and the optimal threshold is characterised as a solution of a (typically nonlinear) equation. The main ingredient we use is a representation result for excessive functions in terms of expected suprema.

Gradient refinement methods for optimal impulse control problems

2011 ◽  
Vol 72 (10) ◽  
pp. 2188-2195 ◽  
Author(s):  
E. V. Goncharova ◽  
M. V. Staritsyn
Keyword(s):  
Impulse Control ◽  
Control Problems ◽  
Optimal Impulse

scholarly journals The W,Z/ν,δ Paradigm for the First Passage of Strong Markov Processes without Positive Jumps

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 18 ◽  
Author(s):  
Florin Avram ◽  
Danijel Grahovac ◽  
Ceren Vardar-Acar
Keyword(s):  
Variational Problem ◽  
Markov Processes ◽  
Risk Control ◽  
Stopping Time ◽  
Control Problems ◽  
Unified Framework ◽  
First Passage ◽  
Scale Functions ◽  
Basic Functions ◽  
Strong Markov

As is well-known, the benefit of restricting Lévy processes without positive jumps is the “ W , Z scale functions paradigm”, by which the knowledge of the scale functions W , Z extends immediately to other risk control problems. The same is true largely for strong Markov processes X t , with the notable distinctions that (a) it is more convenient to use as “basis” differential exit functions ν , δ , and that (b) it is not yet known how to compute ν , δ or W , Z beyond the Lévy, diffusion, and a few other cases. The unifying framework outlined in this paper suggests, however, via an example that the spectrally negative Markov and Lévy cases are very similar (except for the level of work involved in computing the basic functions ν , δ ). We illustrate the potential of the unified framework by introducing a new objective () for the optimization of dividends, inspired by the de Finetti problem of maximizing expected discounted cumulative dividends until ruin, where we replace ruin with an optimally chosen Azema-Yor/generalized draw-down/regret/trailing stopping time. This is defined as a hitting time of the “draw-down” process Y t = sup 0 ≤ s ≤ t X s - X t obtained by reflecting X t at its maximum. This new variational problem has been solved in a parallel paper.

Averaging problems of running processes associated with Brownian motion and applications

2015 ◽  
Vol 26 (03) ◽  
pp. 1550028
Author(s):  
Bao Quoc Ta
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Markov Processes ◽  
Optimal Stopping ◽  
Explicit Solutions ◽  
Reflecting Brownian Motion ◽  
Crucial Feature ◽  
Excessive Functions ◽  
Optimal Stopping Problems ◽  
Strong Markov

Recently the new technique to solve optimal stopping problems for Hunt processes is developed (see [S. Christensen, P. Salminen and B. Q. Ta, Optimal stopping of strong Markov processes, Stochastic Process. Appl. 123(3) (2013) 1138–1159]). The crucial feature of the approach is to utilize the representation of the r-excessive functions as expected suprema. However, it seems to be difficult when applying directly the approach to some concrete cases, e.g. one-sided problem for reflecting Brownian motion and two-sided problem for Brownian motion. In this paper, we review and exploit this approach to find explicit solutions of two problems above.

scholarly journals Childhood Reports of Food Neglect and Impulse Control Problems and Violence in Adulthood

2016 ◽  
Vol 13 (4) ◽  
pp. 389 ◽  
Author(s):  
Michael Vaughn ◽  
Christopher Salas-Wright ◽  
Sandra Naeger ◽  
Jin Huang ◽  
Alex Piquero
Keyword(s):  
Impulse Control ◽  
Control Problems
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