Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-16T15:07:02.550Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Stopping Problem with Controlled Recall

Published online by Cambridge University Press:  27 July 2009

Tsuyoshi Saito
Tsuyoshi Saito
Affiliation:
Doctoral Program in Policy and Planning Sciences, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with the following discrete-time optimal stopping problem. For fixed search costs, a random offer, w ~ F(w), will be found for each time. This offer is either accepted, rejected, or “reserved” for recall later. The reserving cost for any offer depends on its value, regardless of how long the offer is reserved. The objective is to maximize the expected discounted net profit, provided that an offer must be accepted. The major finding is that no previously reserved offer should be accepted prior to the deadline of the search process.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 1 , January 1998 , pp. 91 - 108
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chow, Y.S., Robbins, H., & Siegmund, D. (1991). The theory of optimal stopping. New York: Dover Publications.Google Scholar
2.Chun, Y.H. (1996). Selecting the best choice in the weighted secretary problem. European Journal of Operational Research 92: 135–147.CrossRefGoogle Scholar
3.Hill, P. & Krengel, U. (1991). Minimax-optimal stop rules and distributions in secretary problems. The Annals of Probability 19: 342–353.CrossRefGoogle Scholar
4.Ikuta, S. (1988). Optimal stopping problem with uncertain recall. Journal of the Operations Research Society of Japan 31: 145–170.CrossRefGoogle Scholar
5.Ikuta, S. (1992). The optimal stopping problem in which the sum of the accepted offer's value and the remaining search budget is an objective function. Journal of the Operations Research Society of Japan 35: 172–193.CrossRefGoogle Scholar
6.Ikuta, S. (1994). Markovian decision processes and its application of economic and managerial problems. Unpublished lecture note.Google Scholar
7.Ikuta, S. (1995). The optimal stopping problem with several search areas. Journal of the Operations Research Society of Japan 38:89–106.CrossRefGoogle Scholar
8.Karlin, S. (1962). Stochastic models and optimal policy for selling an asset. In Karlin, S., Arrow, K.J., & Scarf, H. (eds.), Studies in applied probability and management science. Stanford, CA: Stanford University Press, Chap. 9, pp. 148–158.Google Scholar
9.Kami, E. & Schwartz, A. (1977). Search theory: The case of search with uncertain recall. Journal of Economic Theory 16: 38–52.Google Scholar
10.Kohn, M.G. & Shavell, S. (1974). The theory of search. Journal of Economic Theory 9: 93–123.CrossRefGoogle Scholar
11.Landsberger, M. & Peled, D. (1977). Duration of offers, price structure, and the gain from search. Journal of Economic Theory 16: 17–37.CrossRefGoogle Scholar
12.Lippman, S.A. & McCall, J.J. (1976). Job search in a dynamic economy. Journal of Economic Theory 12: 365–390.CrossRefGoogle Scholar
13.Lorenzen, T.J. (1981). Optimal stopping with sampling cost: The secretary problem. The Annals of Probability 9: 167–172.CrossRefGoogle Scholar
14.McCall, J.J. (1965). The economics of information and optimal stopping rules. Journal of Business 38:300–317.CrossRefGoogle Scholar
15.Morgan, P. & Manning, R. (1985). Optimal search. Econometrica 53: 923–944.CrossRefGoogle Scholar
16.Petrucelli, J.D. (1981). Best choice problems involving uncertainty and recall of observations. Journal of Applied Probability 18: 415–425.CrossRefGoogle Scholar
17.Petrucelli, J.D. (1982). Full information best choice problems with recall of observations and uncertainty of selection depending on the observation. Advances in Applied Probability 14: 340–358.CrossRefGoogle Scholar
18.Rosenfield, D.B., Shapiro, R.D., & Butler, D.A. (1983). Optimal strategies for selling an asset. Management Science 29: 1051–1061.CrossRefGoogle Scholar
19.Ross, S.M. (1969). A problem in optimal search and stop. Operations Research 17: 984–992.CrossRefGoogle Scholar
20.Rothschild, M. (1974). Searching for the lowest price when the distribution of prices is unknown. Journal of Political Economy 82: 689–711.CrossRefGoogle Scholar
21.Sakaguchi, M. (1961). Dynamic programming of some sequential sampling design. Journal of Mathematical Analysis and Applications 2:446–466.CrossRefGoogle Scholar
22.Samuel-Chan, E. (1995). The best choice secretary problem with random freeze on jobs. Stochastic Processes and Their Applications 55: 315–327.CrossRefGoogle Scholar
23.Sun, M. (1992). Nested variational inequalities and related optimal starting-stopping problems. Journal of Applied Probability 29: 104–115.CrossRefGoogle Scholar
24.Taylor, H.M. (1967). Evaluating a call option and optimal timing strategy in the stock market. Management Science 14: 111–120.CrossRefGoogle Scholar
25.Weitzman, M.L. (1979). Optimal search for the best alternative. Econometrica 47: 641–654.CrossRefGoogle Scholar