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Optimal Stopping Problem with Controlled Recall

  • Tsuyoshi Saito (a1)
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.

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2.Y.H. Chun (1996). Selecting the best choice in the weighted secretary problem. European Journal of Operational Research 92: 135147.

3.P. Hill & U. Krengel (1991). Minimax-optimal stop rules and distributions in secretary problems. The Annals of Probability 19: 342353.

10.M.G. Kohn & S. Shavell (1974). The theory of search. Journal of Economic Theory 9: 93123.

11.M. Landsberger & D. Peled (1977). Duration of offers, price structure, and the gain from search. Journal of Economic Theory 16: 1737.

12.S.A. Lippman & J.J. McCall (1976). Job search in a dynamic economy. Journal of Economic Theory 12: 365390.

13.T.J. Lorenzen (1981). Optimal stopping with sampling cost: The secretary problem. The Annals of Probability 9: 167172.

14.J.J. McCall (1965). The economics of information and optimal stopping rules. Journal of Business 38:300317.

15.P. Morgan & R. Manning (1985). Optimal search. Econometrica 53: 923944.

16.J.D. Petrucelli (1981). Best choice problems involving uncertainty and recall of observations. Journal of Applied Probability 18: 415425.

17.J.D. Petrucelli (1982). Full information best choice problems with recall of observations and uncertainty of selection depending on the observation. Advances in Applied Probability 14: 340358.

18.D.B. Rosenfield , R.D. Shapiro , & D.A. Butler (1983). Optimal strategies for selling an asset. Management Science 29: 10511061.

19.S.M. Ross (1969). A problem in optimal search and stop. Operations Research 17: 984992.

20.M. Rothschild (1974). Searching for the lowest price when the distribution of prices is unknown. Journal of Political Economy 82: 689711.

21.M. Sakaguchi (1961). Dynamic programming of some sequential sampling design. Journal of Mathematical Analysis and Applications 2:446466.

22.E. Samuel-Chan (1995). The best choice secretary problem with random freeze on jobs. Stochastic Processes and Their Applications 55: 315327.

23.M. Sun (1992). Nested variational inequalities and related optimal starting-stopping problems. Journal of Applied Probability 29: 104115.

24.H.M. Taylor (1967). Evaluating a call option and optimal timing strategy in the stock market. Management Science 14: 111120.

25.M.L. Weitzman (1979). Optimal search for the best alternative. Econometrica 47: 641654.

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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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