scholarly journals On general optimal stopping problems using penalty method

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Ł. Stettner
Keyword(s):  
Stochastic Processes ◽  
Markov Processes ◽  
Discrete Time ◽  
Optimal Stopping ◽  
Penalty Method ◽  
Value Function ◽  
Polish Space ◽  
Finite Horizon ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Problems

AbstractIn the paper we use penalty method to approximate a number of general stopping problems over finite horizon. We consider optimal stopping of discrete time or right continuous stochastic processes, and show that suitable version of Snell’s envelope can by approximated by solutions to penalty equations. Then we study optimal stopping problem for Markov processes on a general Polish space, and again show that the optimal stopping value function can be approximated by a solution to a Markov version of the penalty equation.

scholarly journals Partially observed optimal stopping problem for discrete-time Markov processes

4OR ◽  
2016 ◽  
Vol 15 (3) ◽  
pp. 277-302 ◽  
Author(s):  
Benoîte de Saporta ◽  
François Dufour ◽  
Christophe Nivot
Keyword(s):  
Markov Processes ◽  
Discrete Time ◽  
Optimal Stopping ◽  
Optimal Stopping Problem ◽  
Partially Observed

scholarly journals Value Function and Optimal Rule on the Optimal Stopping Problem for Continuous-Time Markov Processes

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Lu Ye
Keyword(s):  
Explicit Formula ◽  
Markov Processes ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Value Function ◽  
Broad Class ◽  
Stopping Time ◽  
Optimal Stopping Problem ◽  
Optimal Rule ◽  
Reward Functions

This paper considers the optimal stopping problem for continuous-time Markov processes. We describe the methodology and solve the optimal stopping problem for a broad class of reward functions. Moreover, we illustrate the outcomes by some typical Markov processes including diffusion and Lévy processes with jumps. For each of the processes, the explicit formula for value function and optimal stopping time is derived. Furthermore, we relate the derived optimal rules to some other optimal problems.

scholarly journals Optimal Selling Rule in a Regime Switching Lévy Market

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Moustapha Pemy
Keyword(s):  
Variational Inequalities ◽  
Viscosity Solution ◽  
Optimal Stopping ◽  
Regime Switching ◽  
Stock Price ◽  
Value Function ◽  
Markov Switching ◽  
Finite Horizon ◽  
Optimal Stopping Problem ◽  
Numerical Example

This paper is concerned with a finite-horizon optimal selling rule problem when the underlying stock price movements are modeled by a Markov switching Lévy process. Assuming that the transaction fee of the selling operation is a function of the underlying stock price, the optimal selling rule can be obtained by solving an optimal stopping problem. The corresponding value function is shown to be the unique viscosity solution to the associated HJB variational inequalities. A numerical example is presented to illustrate the results.

scholarly journals A Forward Algorithm for Solving Optimal Stopping Problems

2006 ◽  
Vol 43 (01) ◽  
pp. 102-113
Author(s):  
Albrecht Irle
Keyword(s):  
State Space ◽  
Optimal Stopping ◽  
Stopping Time ◽  
The State ◽  
Optimal Stopping Problem ◽  
Forward Algorithm ◽  
Optimal Stopping Time ◽  
Entrance Time ◽  
Markov Sequence ◽  
Optimal Stopping Problems

We consider the optimal stopping problem for g(Z n ), where Z n , n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B 0 ⊇ B 1 ⊇ B 2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.

scholarly journals On sufficient statistics for optimal stopping problems of stochastic processes

1971 ◽  
Vol 11 (3) ◽  
pp. 529-533
Author(s):  
B. Grigelionis
Keyword(s):  
Stochastic Processes ◽  
Optimal Stopping ◽  
Sufficient Statistics ◽  
Optimal Stopping Problems

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. И. Григелионис. К вопросу о достаточных статистиках для задач об оптимальной остановке случайных процессов B. Grigelionis. Pakankamų statistikų atsitiktinių procesų optimalaus sustabdymo uždaviniams klausimu

scholarly journals American options in an imperfect complete market with default

2018 ◽  
Vol 64 ◽  
pp. 93-110 ◽  
Author(s):  
Roxana Dumitrescu ◽  
Marie-Claire Quenez ◽  
Agnès Sulem
Keyword(s):  
Optimal Stopping ◽  
Value Function ◽  
American Options ◽  
American Option ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Nonlinear Expectation ◽  
Portfolio Strategy ◽  
Reflected Bsde ◽  
The Value Function

We study pricing and hedging for American options in an imperfect market model with default, where the imperfections are taken into account via the nonlinearity of the wealth dynamics. The payoff is given by an RCLL adapted process (ξt). We define the seller's price of the American option as the minimum of the initial capitals which allow the seller to build up a superhedging portfolio. We prove that this price coincides with the value function of an optimal stopping problem with a nonlinear expectation 𝓔g (induced by a BSDE), which corresponds to the solution of a nonlinear reflected BSDE with obstacle (ξt). Moreover, we show the existence of a superhedging portfolio strategy. We then consider the buyer's price of the American option, which is defined as the supremum of the initial prices which allow the buyer to select an exercise time τ and a portfolio strategy φ so that he/she is superhedged. We show that the buyer's price is equal to the value function of an optimal stopping problem with a nonlinear expectation, and that it can be characterized via the solution of a reflected BSDE with obstacle (ξt). Under the additional assumption of left upper semicontinuity along stopping times of (ξt), we show the existence of a super-hedge (τ, φ) for the buyer.

Sign in / Sign up

Export Citation Format

Share Document