scholarly journals Lagrangian Discretization of Crowd Motion and Linear Diffusion

2020 ◽  
Vol 58 (4) ◽  
pp. 2093-2118 ◽  
Author(s):  
Hugo Leclerc ◽  
Quentin Mérigot ◽  
Filippo Santambrogio ◽  
Federico Stra
Keyword(s):  
Linear Diffusion ◽  
Crowd Motion

scholarly journals Ergodic control of diffusions with random intervention times

2021 ◽  
Vol 58 (1) ◽  
pp. 1-21
Author(s):  
Harto Saarinen ◽  
Jukka Lempa
Keyword(s):  
Optimal Solution ◽  
Singular Control ◽  
Control Policy ◽  
Control Problems ◽  
Ergodic Control ◽  
Linear Diffusion ◽  
One Dimensional ◽  
And Diffusion ◽  
Independent Poisson Process ◽  
Exact Amount

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

Optimal Stopping of the Maximum Process

2014 ◽  
Vol 51 (03) ◽  
pp. 818-836 ◽  
Author(s):  
Luis H. R. Alvarez ◽  
Pekka Matomäki
Keyword(s):  
Brownian Motion ◽  
Free Boundary ◽  
Optimal Stopping ◽  
Original Problem ◽  
Alternative Route ◽  
Linear Diffusion ◽  
Maximum Process ◽  
Running Maximum ◽  
Parameterized Family ◽  
Optimal Stopping Problems

We consider a class of optimal stopping problems involving both the running maximum as well as the prevailing state of a linear diffusion. Instead of tackling the problem directly via the standard free boundary approach, we take an alternative route and present a parameterized family of standard stopping problems of the underlying diffusion. We apply this family to delineate circumstances under which the original problem admits a unique, well-defined solution. We then develop a discretized approach resulting in a numerical algorithm for solving the considered class of stopping problems. We illustrate the use of the algorithm in both a geometric Brownian motion and a mean reverting diffusion setting.

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