continuous martingale (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/ kənˈtɪn.ju.əs ˌmɑːr.tɪˈɡeɪl /

Meaning and Usage

A continuous martingale is a concept from probability theory and stochastic processes, particularly in the context of financial mathematics and statistics. It refers to a type of stochastic process that has the following characteristics:

1. Martingale Property: The expected value of the process at a future time, conditioned on the present value, is equal to the present value. This means there is no "drift" in expected value over time.
2. Continuity: The process evolves continuously over time rather than in discrete time intervals.

Continuous martingales are often used to model fair games or stock prices in finance, where the best prediction of future prices, based on current information, is simply the current price itself.

They are commonly referenced in written academic articles and textbooks, and their usage is prevalent in both oral discussions and lectures within the fields of mathematics, finance, and statistics.

Example Sentences

1. The theory of continuous martingale is essential for understanding modern financial models.

2. Теория непрерывных мартингалов важна для понимания современных финансовых моделей.

3. In stochastic calculus, continuous martingales serve as foundational tools for option pricing.

4. В стохастическом исчислении непрерывные мартингалы служат основными инструментами для оценки опционов.

5. Researchers have shown that many empirical financial time series can be well approximated by continuous martingales.

6. Исследователи показали, что многие эмпирические временные ряды финансов могут быть хорошо аппроксимированы непрерывными мартингалами.

Idiomatic Expressions

While "continuous martingale" itself is not commonly used in idiomatic expressions, the concept of "martingale" appears in various contexts related to probability and fairness. Here are some examples related to "martingale":

1. "The strategy is a martingale approach to betting, meaning that you double your bet after each loss."

2. "Эта стратегия основана на подходе мартингала к ставкам, что означает, что вы удваиваете свою ставку после каждого проигрыша."

3. "In the world of finance, engaging in a martingale scheme can lead to substantial risks with potential rewards."

4. "В мире финансов участие в схеме мартингала может привести к значительным рискам с потенциальными вознаграждениями."

5. "A classic martingale process ensures that you always return to your original investment value."

6. "Классический процесс мартингала гарантирует, что вы всегда вернетесь к своей первоначальной стоимости инвестиции."

Etymology

The term "martingale" originates from the 18th century, specifically from the French word "martingale," which referred to a betting strategy in games of chance. The mathematical use of the term was formalized later in the context of stochastic processes. The "continuous" aspect refers to the nature of the process not being discrete but evolving over continuous time.

Synonyms and Antonyms

Synonyms: - Stochastic process - Fair game (in terms of expected value)

Antonyms: - Biased process - Non-martingale process