scholarly journals Optimal stopping time on discounted semi-Markov processes

2021 ◽  
Author(s):  
Fang Chen ◽  
Xianping Guo ◽  
Zhong-Wei Liao
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Optimal Stopping Time ◽  
Semi Markov Processes

General optimal stopping theorems for semi-Markov processes

1993 ◽  
Vol 25 (4) ◽  
pp. 825-846 ◽  
Author(s):  
Frans A. Boshuizen ◽  
José M. Gouweleeuw
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
General Setting ◽  
The State ◽  
Shock Models ◽  
Special Cases ◽  
Optimal Stopping Problems ◽  
The Times ◽  
Semi Markov Processes

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made.Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases.The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].

General optimal stopping theorems for semi-Markov processes

1993 ◽  
Vol 25 (04) ◽  
pp. 825-846 ◽  
Author(s):  
Frans A. Boshuizen ◽  
José M. Gouweleeuw
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Stopping Time ◽  
General Setting ◽  
The State ◽  
Shock Models ◽  
Special Cases ◽  
Optimal Stopping Problems ◽  
The Times ◽  
Semi Markov Processes

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made. Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases. The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

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.

ε - Optimal Stopping Time for Genetic Algorithms

1998 ◽  
Vol 35 (1-4) ◽  
pp. 91-111 ◽  
Author(s):  
C.A. Murthy ◽  
Dinabandhu Bhandari ◽  
Sankar K. Pal
Keyword(s):  
Genetic Algorithms ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Optimal Stopping Time

Optimal stopping time with stochastic volatility

2014 ◽  
Vol 41 ◽  
pp. 319-328 ◽  
Author(s):  
Ran Zhang ◽  
Shuang Xu
Keyword(s):  
Stochastic Volatility ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Optimal Stopping Time

On Pricing American Put Option on a Fixed Term: A Monte Carlo Approach

2021 ◽  
pp. 2050010
Author(s):  
Perpetual Andam Boiquaye
Keyword(s):  
Monte Carlo ◽  
Optimal Stopping ◽  
Geometric Mean ◽  
Option Price ◽  
Stopping Time ◽  
Optimal Stopping Time ◽  
American Put Option ◽  
Put Option ◽  
One Year ◽  
American Put

This paper focuses primarily on pricing an American put option with a fixed term where the price process is geometric mean-reverting. The change of measure is assumed to be incorporated. Monte Carlo simulation was used to calculate the price of the option and the results obtained were analyzed. The option price was found to be $94.42 and the optimal stopping time was approximately one year after the option was sold which means that exercising early is the best for an American put option on a fixed term. Also, the seller of the put option should have sold $0.01 assets and bought $ 95.51 bonds to get the same payoff as the buyer at the end of one year for it to be a zero-sum game. In the simulation study, the parameters were varied to see the influence it had on the option price and the stopping time and it showed that it either increases or decreases the value of the option price and the optimal stopping time or it remained unchanged.

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