Search results for "Optimal stopping"
showing 8 items of 8 documents
American Option Pricing and Exercising with Transaction Costs
2005
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal tra…
Performance of adaptive sample size adjustment with respect to stopping criteria and time of interim analysis
2006
The benefit of adjusting the sample size in clinical trials on the basis of treatment effects observed in interim analysis has been the subject of several recent papers. Different conclusions were drawn about the usefulness of this approach for gaining power or saving sample size, because of differences in trial design and setting. We examined the benefit of sample size adjustment in relation to trial design parameters such as 'time of interim analysis' and 'choice of stopping criteria'. We compared the adaptive weighted inverse normal method with classical group sequential methods for the most common and for optimal stopping criteria in early, half-time and late interim analyses. We found …
Optimal selection of the four best of a sequence
1993
We consider the situation in which the decision-maker is allowed to have four choices with purpose to choose exactly the four absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right choice are given for largeN∈N, the maximum asymptotic value of the best choice being limN→∞P(win)≈0.12706.
Portfolio optimisation with strictly positive transaction costs and impulse control
1998
One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…
Stochastic Decision Support Models and Optimal Stopping Rules in a New Product Lifetime Testing
2010
Determining when to stop a statistical test is an important management decision. Several stopping criteria have been proposed, including criteria based on statistical similarity, the probability that the system has a desired reliability, and the expected cost of remaining faults. This paper presents a new stopping rule in fixed-sample testing based on the statistical estimation of total costs involved in the decision to continue beyond an early failure as well as a stopping rule in sequential-sample testing to determine when testing should be stopped. The paper considers the problem that can be stated as follows. A new product is submitted for lifetime testing. The product will be accepted …
The best choice problem with an unknown number of objects
1993
The secretary problem with a known prior distribution of the number of candidates is considered. Ifp(i)=p(N=i),i ∈ [α, β] ∩ ℕ, whereα=inf{i ∈ℕ:p(i) > 0} andβ=sup{i ∈ℕ:p(i)≳0}, is the prior distribution of the numberN of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping indexj=minΓ satisfies asymptotically (asβ → ∞) the equationj=exp $${{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} {\left. {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i)/i} } \right) - 1} \ri…
Optimal selection of thek best of a sequence withk stops
1997
We first consider the situation in which the decision-maker is allowed to have five choices with purpose to choose exactly the five absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right five-choice are given for largeN eN, the maximum asymptotic value of the probability of the best choice being limN→∝P (win) ≈ 0.104305. Then, we study the general problem of selecting thek best of a sequence withk stops, constructing first a rough solution for this problem. Using this suboptimal solution, we find an approximation for the optimal probability valuesPk of the form $$P_k \approx \frac{1}{{(e - 1)k + 1}}$$ for any k eN.
Optimal Impulse Control When Control Actions Have Random Consequences
1997
We consider a generalised impulse control model for controlling a process governed by a stochastic differential equation. The controller can only choose a parameter of the probability distribution of the consequence of his control action which is therefore random. We state optimality results relating the value function to quasi-variational inequalities and a formal optimal stopping problem. We also remark that the value function is a viscosity solution of the quasi-variational inequalities which could lead to developments and convergence proofs of numerical schemes. Further, we give some explicit examples and an application in financial mathematics, the optimal control of the exchange rate…