scholarly journals Solving finite time horizon Dynkin games by optimal switching

2016 ◽  
Vol 53 (4) ◽  
pp. 957-973 ◽  
Author(s):  
Randall Martyr
Keyword(s):  
Time Horizon ◽  
Sufficient Conditions ◽  
Optimal Switching ◽  
Put Options ◽  
Norm Estimates ◽  
Dynkin Games ◽  
Dynkin Game ◽  
Special Cases ◽  
Black Scholes ◽  
Finite Time Horizon

Abstract This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black‒Scholes market.

scholarly journals The effect of consolidated periods in heterogeneous lot-sizing games

Top ◽  
2021 ◽  
Author(s):  
Luis A. Guardiola ◽  
Ana Meca ◽  
Justo Puerto
Keyword(s):  
Time Horizon ◽  
Lot Sizing ◽  
Sufficient Conditions ◽  
Minimum Cost ◽  
Cost Allocations ◽  
Lot Sizing Problem ◽  
Stable Family ◽  
Finite Time Horizon ◽  
The Stability ◽  
Operation Cost

AbstractWe consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the members of the coalitions. This implies that each firm uses the best ordering channel and holding technology provided by the participants in the consortium. That is, they produce, hold inventory, pay backlogged demand and make orders at the minimum cost of the coalition members. Thus, firms aim at satisfying their demand over the planing horizon with minimal operation cost. Our contribution is to show that there exist fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. Then we propose a parametric family of cost allocations and provide sufficient conditions for this to be a stable family against coalitional defections of firms. Finally, we focus on those periods of the time horizon that are consolidated and we analyze their effect on the stability of cost allocations.

Russian options with a finite time horizon

2004 ◽  
Vol 41 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Optimal Stopping ◽  
Finite Time ◽  
Time Horizon ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Finite Time Horizon ◽  
Russian Option

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

scholarly journals Optimal Jamming Attack Scheduling in Networked Sensing and Control Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Lifu Zhang ◽  
Heng Zhang ◽  
Cunhua Li ◽  
Buxi Ni
Keyword(s):  
Control Systems ◽  
Time Horizon ◽  
Linear Quadratic ◽  
Control Cost ◽  
Linear Quadratic Gaussian ◽  
Jamming Attack ◽  
Special Cases ◽  
Finite Time Horizon ◽  
And Control ◽  
The Given

This paper investigates the optimal jamming attack scheduling in Networked Sensing and Control Systems (NSCS). From viewpoint of the attacker, we formulate an optimization problem which maximizes the Linear Quadratic Gaussian (LQG) control cost with attacking energy constraint in a finite time horizon. For two special cases, we obtain that the optimal jamming attack schedule is to consecutively attack in the given time horizon. For the general case, we propose an algorithm to find the optimal schedules. Finally, we study the effectiveness of our proposed attack strategies on our established semiphysical testbed.

Russian options with a finite time horizon

2004 ◽  
Vol 41 (02) ◽  
pp. 313-326 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Optimal Stopping ◽  
Finite Time ◽  
Time Horizon ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Finite Time Horizon ◽  
Russian Option

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1466
Author(s):  
Beatris Adriana Escobedo-Trujillo ◽  
José Daniel López-Barrientos ◽  
Javier Garrido-Meléndez
Keyword(s):  
Dynamic Programming ◽  
Dirichlet Problem ◽  
Stochastic Control ◽  
Finite Time ◽  
Time Horizon ◽  
Closed Loop ◽  
Programming Techniques ◽  
Pollution Accumulation ◽  
Finite Time Horizon ◽  
The Cost

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

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