Optimal and adaptive stopping based on capture times

1974 ◽  
Vol 11 (02) ◽  
pp. 294-301 ◽  
Author(s):  
Norman Starr
Keyword(s):  
Optimal Stopping ◽  
Linear Time ◽  
Stopping Time ◽  
Statistical Procedure ◽  
Time Cost ◽  
Expected Payoff ◽  
Optimal Stopping Time

Independent exponential capture times are assumed for each of N prey. The payoff is the number of prey caught less a linear time cost. The optimal stopping time and value are obtained. When N is known an adaptive statistical procedure is proposed for which the expected payoff differs from the value by at most one-half plus a term which tends to zero (of order N –α, a < 1) as N → ∞.

Optimal and adaptive stopping based on capture times

1974 ◽  
Vol 11 (2) ◽  
pp. 294-301 ◽  
Author(s):  
Norman Starr
Keyword(s):  
Optimal Stopping ◽  
Linear Time ◽  
Stopping Time ◽  
Statistical Procedure ◽  
Time Cost ◽  
Expected Payoff ◽  
Optimal Stopping Time

Independent exponential capture times are assumed for each of N prey. The payoff is the number of prey caught less a linear time cost. The optimal stopping time and value are obtained. When N is known an adaptive statistical procedure is proposed for which the expected payoff differs from the value by at most one-half plus a term which tends to zero (of order N–α, a < 1) as N → ∞.

Some asymptotic results for optimal stopping based on capture times

1976 ◽  
Vol 13 (4) ◽  
pp. 741-750
Author(s):  
Robert L. Wardrop
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Linear Time ◽  
Random Time ◽  
Time Cost ◽  
Asymptotic Results ◽  
Expected Payoff

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Zi; where Z1, Z2, …, Zn are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

Some asymptotic results for optimal stopping based on capture times

1976 ◽  
Vol 13 (04) ◽  
pp. 741-750
Author(s):  
Robert L. Wardrop
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Linear Time ◽  
Random Time ◽  
Time Cost ◽  
Asymptotic Results ◽  
Expected Payoff

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Z i; where Z 1, Z 2, …, Z n are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

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

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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