scholarly journals A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis

2013 ◽  
Author(s):  
Tiziano De Angelis ◽  
Giorgio Ferrari
Keyword(s):  
Free Boundary ◽  
Finite Time ◽  
Time Horizon ◽  
Boundary Analysis ◽  
Investment Problem ◽  
Finite Time Horizon

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.

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.

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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