Triple

T22150832
Position Surface form Disambiguated ID Type / Status
Subject Freddy Delbaen E547406 entity
Predicate notableWork P4 FINISHED
Object “The Mathematics of Arbitrage”
“The Mathematics of Arbitrage” is a rigorous mathematical finance text that develops the theory of arbitrage-free markets and pricing using modern probability and measure-theoretic tools.
E1522148 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: “The Mathematics of Arbitrage” | Statement: [Freddy Delbaen, notableWork, “The Mathematics of Arbitrage”]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: “The Mathematics of Arbitrage”
Context triple: [Freddy Delbaen, notableWork, “The Mathematics of Arbitrage”]
  • A. Rabin’s calibration theorem for expected utility
    Rabin’s calibration theorem for expected utility is a result in behavioral economics showing that standard expected utility theory with concave utility cannot plausibly explain observed levels of risk aversion over small stakes without implying absurdly high risk aversion over large stakes.
  • B. Merton’s model of credit risk
    Merton’s model of credit risk is a structural framework in finance that values a firm’s equity as a call option on its assets to assess the probability of default and price corporate debt.
  • C. Merton’s jump-diffusion model
    Merton’s jump-diffusion model is a financial model that extends the Black–Scholes framework by incorporating sudden, random price jumps in addition to continuous diffusion to better capture real-world asset price dynamics.
  • D. Lucas asset pricing model
    The Lucas asset pricing model is a foundational rational expectations framework in macro-finance that explains asset prices through representative-agent intertemporal consumption choices under uncertainty.
  • E. Burkholder–Davis–Gundy inequalities
    The Burkholder–Davis–Gundy inequalities are fundamental results in stochastic analysis that provide two-sided bounds relating the moments of martingales to the moments of their quadratic variation.
  • 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: “The Mathematics of Arbitrage”
Triple: [Freddy Delbaen, notableWork, “The Mathematics of Arbitrage”]
Generated description
“The Mathematics of Arbitrage” is a rigorous mathematical finance text that develops the theory of arbitrage-free markets and pricing using modern probability and measure-theoretic tools.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: “The Mathematics of Arbitrage”
Target entity description: “The Mathematics of Arbitrage” is a rigorous mathematical finance text that develops the theory of arbitrage-free markets and pricing using modern probability and measure-theoretic tools.
  • A. Rabin’s calibration theorem for expected utility
    Rabin’s calibration theorem for expected utility is a result in behavioral economics showing that standard expected utility theory with concave utility cannot plausibly explain observed levels of risk aversion over small stakes without implying absurdly high risk aversion over large stakes.
  • B. Merton’s model of credit risk
    Merton’s model of credit risk is a structural framework in finance that values a firm’s equity as a call option on its assets to assess the probability of default and price corporate debt.
  • C. Merton’s jump-diffusion model
    Merton’s jump-diffusion model is a financial model that extends the Black–Scholes framework by incorporating sudden, random price jumps in addition to continuous diffusion to better capture real-world asset price dynamics.
  • D. Lucas asset pricing model
    The Lucas asset pricing model is a foundational rational expectations framework in macro-finance that explains asset prices through representative-agent intertemporal consumption choices under uncertainty.
  • E. Burkholder–Davis–Gundy inequalities
    The Burkholder–Davis–Gundy inequalities are fundamental results in stochastic analysis that provide two-sided bounds relating the moments of martingales to the moments of their quadratic variation.
  • 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_69e11e3b52088190ad5df386d01eb2fb completed April 16, 2026, 5:36 p.m.
NER Named-entity recognition batch_69f129f37dac8190a7cecb12f4271515 completed April 28, 2026, 9:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0a9704f4988190b03783c006929ad7 completed May 18, 2026, 4:35 a.m.
NEDg Description generation batch_6a0a97e509a88190a7f316cf340d010a completed May 18, 2026, 4:39 a.m.
NED2 Entity disambiguation (via description) batch_6a0a987daa208190bab5b7adec1913e8 completed May 18, 2026, 4:41 a.m.
Created at: April 16, 2026, 8:33 p.m.