[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83598-en":3,"doc-seo-83598-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83598,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Asymmetric Trading Prophets","The “Trading Prophet” problem studies how an online trader can maximize profit by buying and selling under stochastic prices and storage limits against an offline prophet with full foresight. Prior work assumed a single shared price and tightly coupled buy/sell decisions, which misses asymmetry in decentralized dealer-style markets. The document introduces Asymmetric Trading Prophets, where each time step reveals a (bt, st) tuple for buy cost and sell revenue that may be arbitrarily correlated, then analyzes competitive profit versus capacity and initial inventory.","arXiv :2607 .0 15 16v 1 [ cs .DS] 1 Jul 2026  \nAsymmetric Trading Prophets  \nGagan Aggarwal∗ Anupam Gupta† Yifan Wang‡ Mingfei Zhao§  \nJuly 3, 2026  \nAbstract  \nThe “Trading Prophet” problem challenges an online trader to maximize its profit by buying and selling assets under stochastic prices and capacity constraints, competing against an offline prophet with full foresight. In previous work, each arriving asset was assumed to have a single price pt , and the trader was allowed to either buy a copy at this price (subject to having available capacity), or sell a copy (if it already held at least one copy in hand) . However, this abstraction can fail to capture the structural asymmetry of decentralized dealer-based markets, where buying and selling opportunities could be distinct, and driven by individual preferences. To address this, we introduce the Asymmetric Trading Prophets problem, where at each timestep the trader observes a price tuple (bt , st)—representing the cost to buy, and the revenue from selling at this timestep. Importantly, the (bt , st ) tuple could be potentially arbitrarily correlated.  \nWe provide the first competitive analysis for this asymmetric trading prophets problem, characterizing the achievable profit based on the trader’s capacity B and initial inventory B0 . For the unit-capacity case of B = 1, we design online algorithms that achieve constant competitive ratios for both i.i.d. and non-i.i.d. distributions on the price tuples, when the trader has one initial copy (B0 = 1) . For the general capacity case where B can be large, we give algorithms for i.i.d. distributions that achieve a competitive ratio of 1 − Θ(log B0 / √B0  ) . Finally, for the symmetric case (where the price tuple satisfies bt = st ), we improve this to get a competitive ratio of 1 − O(log B/ √B  ), demonstrating that the performance approaches optimality as the capacity increases. We show that both ratios are tight up to a logarithmic factor.  \n∗ Google Research ([gagana@google.com](gagana@google.com)).  \n†Department of Computer Science, New York University. ([anupam.g@nyu.edu](anupam.g@nyu.edu)) Work supported in part by NSF awards CCF-2422926 and CCF-2608359 .  \n‡School of Computer Science, Georgia Tech ([ywang3782@gatech.edu](ywang3782@gatech.edu)) . Part of this work was done while the author was visiting Google as a Student Researcher.  \n§Google Research ([mingfei@google.com](mingfei@google.com)) .  \n1 Introduction  \nThe maxim “buy low, sell high” captures the fundamental goal of any trader, yet executing this strategy in an online setting involves significant uncertainty. This challenge is formally captured by the Trading Prophets problem, introduced by [CCD+23] . In this setting, a trader observes a sequence of stochastic prices for the same asset; they must decide, irrevocably and in real-time, whether to buy a copy of the asset (if they have available capacity) or to sell a copy (if they have at least one copy they can sell), to maximize profit within storage constraints. The objective is to design online algorithms that compete against the “prophet”—an offline benchmark with full foresight of future price realizations. This framework bridges the classic theory of prophet inequalities and optimal stopping with the dynamics of inventory management.  \nThe work by [CCD+23] and [ABLV26] has established strong theoretical foundations for this problem. These works model the market as an exogenous ticker tape: at any time step t, there is a single “market price” drawn from a known distribution. The trader chooses to transact (either buy or sell) at this price. This abstraction effectively models centralized exchanges, such as the stock market, where a unified price dictates terms for all participants and the cost to buy is tightly coupled to the revenue from selling.  \nHowever, this “single price” abstraction fails to capture the structural asymmetry inherent in other decentralized or dealer-based markets. In these settings, a","cbCaieKWJCGeyrIf","https://ap.wps.com/l/cbCaieKWJCGeyrIf","pdf",644635,5,1,37,"English","en",105,"# Abstract\n# Introduction\n## Trading Prophet background\n## Limitations of single-price models\n## Asymmetric Trading Prophet model\n## Key questions and capacity considerations","[{\"question\":\"What problem does “Trading Prophet” aim to solve in an online trading setting?\",\"answer\":\"It maximizes an online trader’s expected profit by making irreversible buy or sell decisions under stochastic prices and storage constraints, while competing against an offline prophet with full future knowledge.\"},{\"question\":\"How does the Asymmetric Trading Prophets (ATP) model extend earlier work?\",\"answer\":\"ATP replaces a single price with a buy/sell price tuple (bt, st) at each timestep, allowing bt and st to be arbitrarily correlated and enabling actions to include buy, sell, or skip.\"},{\"question\":\"What competitive performance results are described for different capacity regimes?\",\"answer\":\"For unit capacity B=1 with initial inventory B0=1, the document designs online algorithms with constant competitive ratios for both i.i.d. and non-i.i.d. distributions. For larger B, it provides i.i.d. guarantees of 1 − Θ(log B0/√B0), improves the symmetric case (bt=st) to 1 − O(log B/√B), and shows tightness up to a logarithmic factor.\"}]",1784189111,93,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"asymmetric-trading-prophets","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/asymmetric-trading-prophets/83598/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does “Trading Prophet” aim to solve in an online trading setting?","Question",{"text":76,"@type":77},"It maximizes an online trader’s expected profit by making irreversible buy or sell decisions under stochastic prices and storage constraints, while competing against an offline prophet with full future knowledge.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the Asymmetric Trading Prophets (ATP) model extend earlier work?",{"text":81,"@type":77},"ATP replaces a single price with a buy/sell price tuple (bt, st) at each timestep, allowing bt and st to be arbitrarily correlated and enabling actions to include buy, sell, or skip.",{"name":83,"@type":74,"acceptedAnswer":84},"What competitive performance results are described for different capacity regimes?",{"text":85,"@type":77},"For unit capacity B=1 with initial inventory B0=1, the document designs online algorithms with constant competitive ratios for both i.i.d. and non-i.i.d. distributions. 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