On the optimal stopping problems with monotone thresholds
As a class of optimal stopping problems with monotone thresholds, we define the candidate-choice problem (CCP) and derive two formulae for calculating its expected payoff. We apply the first formula to a particular CCP, i.e. the best-choice duration problem treated by Ferguson et al. (1992). The rec...
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| Veröffentlicht in: | Journal of applied probability 2015-12, Vol.52 (4), p.926-940 |
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| container_end_page | 940 |
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| container_title | Journal of applied probability |
| container_volume | 52 |
| creator | Tamaki, Mitsushi |
| description | As a class of optimal stopping problems with monotone thresholds, we define the candidate-choice problem (CCP) and derive two formulae for calculating its expected payoff. We apply the first formula to a particular CCP, i.e. the best-choice duration problem treated by Ferguson et al. (1992). The recall case is also examined as a comparison. We also derive the distribution of the stopping time of the CCP and find, as a by-product, that the best-choice problem has a remarkable feature in that the optimal probability of choosing the best is just the expected value of the (proportional) stopping time. The similarity between the best-choice duration problem and the best-choice problem with uniform freeze studied by Samuel-Cahn (1996) is recognized. |
| doi_str_mv | 10.1239/jap/1450802744 |
| format | Article |
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We apply the first formula to a particular CCP, i.e. the best-choice duration problem treated by Ferguson et al. (1992). The recall case is also examined as a comparison. We also derive the distribution of the stopping time of the CCP and find, as a by-product, that the best-choice problem has a remarkable feature in that the optimal probability of choosing the best is just the expected value of the (proportional) stopping time. 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The similarity between the best-choice duration problem and the best-choice problem with uniform freeze studied by Samuel-Cahn (1996) is recognized.</description><subject>60G40</subject><subject>62L15</subject><subject>best-choice duration problem</subject><subject>best-choice problem</subject><subject>Byproducts</subject><subject>candidate-choice problem</subject><subject>duration problem</subject><subject>Expected values</subject><subject>Mathematical analysis</subject><subject>Mathematical problems</subject><subject>monotone rule</subject><subject>Optimization</subject><subject>planar Poisson process</subject><subject>Probability distribution</subject><subject>Recall</subject><subject>Research Papers</subject><subject>Secretary problem</subject><subject>Similarity</subject><subject>Studies</subject><subject>Thresholds</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNptkctLxDAQxoMouD6u3oSCFy_dnbRpHjdl8QULe3HPpWmnuy1tU5MW8b83smUV9ZKByW---fKFkCsKcxrFalFn_YKyBCREgrEjMqNMJCEHER2TGUBEQ-XPU3LmXA3gSSVmRK27YNhhYPqharMmcIPp-6rbBr01usHWBe_VsAta05nBdOhZi25nmsJdkJMyaxxeTvWcbB4fXpfP4Wr99LK8X4V5LBIWSshiXoLQhdBlLIUQirOSUY5RjhKgBK2SQulIIpRSgZRKMEqRKkyk1iw-J3d7Xe-oxnzAMW-qIu2t92s_UpNV6XKzmrpT8VGk31F4iduDxNuIbkjbyuXYNFmHZnQpFZJHEAOXHr35hdZmtJ1_oKeSJAFQHDw131O5Nc5ZLA92KKRfn_HXwfV-oPYB2wPNYslBKuXvYRLMWm2rYos_9v4v-QkQp5TC</recordid><startdate>20151201</startdate><enddate>20151201</enddate><creator>Tamaki, Mitsushi</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20151201</creationdate><title>On the optimal stopping problems with monotone thresholds</title><author>Tamaki, Mitsushi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3754-80a36f07bd7bf38777964f416e2ce800f0b95d9b28e0f8908897411e19e58bb43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>60G40</topic><topic>62L15</topic><topic>best-choice duration problem</topic><topic>best-choice problem</topic><topic>Byproducts</topic><topic>candidate-choice problem</topic><topic>duration problem</topic><topic>Expected values</topic><topic>Mathematical analysis</topic><topic>Mathematical problems</topic><topic>monotone rule</topic><topic>Optimization</topic><topic>planar Poisson process</topic><topic>Probability distribution</topic><topic>Recall</topic><topic>Research Papers</topic><topic>Secretary problem</topic><topic>Similarity</topic><topic>Studies</topic><topic>Thresholds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tamaki, Mitsushi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tamaki, Mitsushi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the optimal stopping problems with monotone thresholds</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>2015-12-01</date><risdate>2015</risdate><volume>52</volume><issue>4</issue><spage>926</spage><epage>940</epage><pages>926-940</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><abstract>As a class of optimal stopping problems with monotone thresholds, we define the candidate-choice problem (CCP) and derive two formulae for calculating its expected payoff. 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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Cambridge University Press Journals Complete |
| subjects | 60G40 62L15 best-choice duration problem best-choice problem Byproducts candidate-choice problem duration problem Expected values Mathematical analysis Mathematical problems monotone rule Optimization planar Poisson process Probability distribution Recall Research Papers Secretary problem Similarity Studies Thresholds |
| title | On the optimal stopping problems with monotone thresholds |
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