Triple

T11961511
Position Surface form Disambiguated ID Type / Status
Subject Robert C. Merton E284678 entity
Predicate notableIdea P4 FINISHED
Object Merton’s portfolio problem
Merton’s portfolio problem is a foundational continuous-time optimization model in financial economics that determines an investor’s optimal consumption and investment strategy under uncertainty.
E956282 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Merton’s portfolio problem | Statement: [Robert C. Merton, notableIdea, Merton’s portfolio problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Merton’s portfolio problem
Context triple: [Robert C. Merton, notableIdea, Merton’s portfolio problem]
  • A. Foundations of a General Theory of Sequential Decision Functions
    Foundations of a General Theory of Sequential Decision Functions is a seminal work in statistics that established the mathematical foundations of sequential analysis and optimal decision-making under uncertainty.
  • B. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • C. Mathematical Theory of Optimal Processes
    Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
  • D. St. Petersburg paradox
    The St. Petersburg paradox is a famous problem in probability theory and economics that highlights how a lottery with an infinite expected payoff can still attract only a finite price from rational gamblers, challenging traditional notions of expected value and decision-making under risk.
  • E. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Merton’s portfolio problem
Triple: [Robert C. Merton, notableIdea, Merton’s portfolio problem]
Generated description
Merton’s portfolio problem is a foundational continuous-time optimization model in financial economics that determines an investor’s optimal consumption and investment strategy under uncertainty.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Merton’s portfolio problem
Target entity description: Merton’s portfolio problem is a foundational continuous-time optimization model in financial economics that determines an investor’s optimal consumption and investment strategy under uncertainty.
  • A. Foundations of a General Theory of Sequential Decision Functions
    Foundations of a General Theory of Sequential Decision Functions is a seminal work in statistics that established the mathematical foundations of sequential analysis and optimal decision-making under uncertainty.
  • B. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • C. Mathematical Theory of Optimal Processes
    Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
  • D. St. Petersburg paradox
    The St. Petersburg paradox is a famous problem in probability theory and economics that highlights how a lottery with an infinite expected payoff can still attract only a finite price from rational gamblers, challenging traditional notions of expected value and decision-making under risk.
  • E. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9037848f481908276716675464464 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f4592fa9a48190a0450e3d0c57c4d3 completed May 1, 2026, 7:41 a.m.
NEDg Description generation batch_69f4645ef63881909b46937f73d637a3 completed May 1, 2026, 8:29 a.m.
NED2 Entity disambiguation (via description) batch_69f465be4db08190882898a17d077019 completed May 1, 2026, 8:35 a.m.
Created at: April 8, 2026, 9:45 p.m.