Triple
T478470
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Itô calculus |
E9112
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object |
Black–Scholes model
The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
|
E59634
|
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: Black–Scholes model | Statement: [Itô calculus, usedIn, Black–Scholes model]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Black–Scholes model Context triple: [Itô calculus, usedIn, Black–Scholes model]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- 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: Black–Scholes model Triple: [Itô calculus, usedIn, Black–Scholes model]
Generated description
The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Black–Scholes model Target entity description: The Black–Scholes model is a fundamental mathematical framework in financial economics for pricing options and other derivatives by modeling asset prices as stochastic processes.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
C.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Girsanov theorem
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
- 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_69a2e7ff81708190b0507a24a997232c |
completed | Feb. 28, 2026, 1:05 p.m. |
| NER | Named-entity recognition | batch_69a2f056459881909749764cc4a7f9e8 |
completed | Feb. 28, 2026, 1:40 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a46804b90881908422851eeb9bbba1 |
completed | March 1, 2026, 4:23 p.m. |
| NEDg | Description generation | batch_69a46901d5c08190af7ea8b01206505c |
completed | March 1, 2026, 4:27 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69a4696c35c08190890e8159983e2efb |
completed | March 1, 2026, 4:29 p.m. |
Created at: Feb. 28, 2026, 1:12 p.m.