Gaussian Process Optimal Stopping for Financial Time Series
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Solution Overview
Problem
Existing methods for optimal stopping problems in finance, such as pricing American options, are limited by the need for restrictive assumptions about independent and identically distributed data, and lack efficient solutions under minimal assumptions, particularly in leveraging Gaussian Process-based algorithms for time series analysis.
Innovation Solution
A Gaussian Process-based algorithm is implemented to determine the optimal time for stopping a sequence of events, using a non-adaptive and adaptive AI approach that estimates potential rewards and value functions based on historical data and recent events, with the ability to model asset prices and quantify uncertainty.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional analytical methods are used for optimal stopping problems, then solutions can be obtained under restrictive assumptions (iid data, known data-generating process), but the methods cannot handle minimal assumptions or complex time series structures
Solution Approach 1:
The patent transforms the optimal stopping problem by changing the parameter representation from raw time series data to Gaussian Process latent variables. This allows the model to handle complex time series structures with minimal assumptions while maintaining tractability through the probabilistic framework of GPs, which can capture mean-reversion and other structural properties without requiring iid assumptions or known data-generating processes.
2Measurement precision
If Gaussian Process-based algorithms are used to model time series with structural properties like mean-reversion, then long term predictions and uncertainty quantification are improved, but computational complexity increases
Solution Approach 1:
The patent segments the time series modeling into two distinct components: a Gaussian Process model that captures long-term structural properties and uncertainty, and an optimal stopping algorithm that operates on the GP predictions. This segmentation allows each component to be optimized independently, reducing overall computational complexity while maintaining prediction accuracy and uncertainty quantification capabilities.
Solution Approach 2:
The Gaussian Process predictions serve as an intermediary between the raw time series data and the optimal stopping decision algorithm. The GP model processes the complex time series structure and outputs simplified predictions with associated uncertainty measures, which then feed into the stopping algorithm. This intermediary role reduces the computational burden on the stopping algorithm while preserving the structural properties of the original data.
3Adaptability or versatility
If Deep GPs are used to automatically choose kernels based on data structure, then adaptability to different data patterns is improved, but the ability to leverage explicit functional forms for efficient optimal stopping solutions is reduced
Solution Approach 1:
The patent performs preliminary action by selecting appropriate Gaussian Process kernels based on known time series structural properties (such as mean-reversion) before applying the optimal stopping algorithm. This preliminary kernel selection leverages explicit functional forms that are known to capture specific time series behaviors, enabling efficient computation while maintaining adaptability to different data patterns through the choice of appropriate kernel functions.
Data Source
AI summary
A method for using a Gaussian Process-based algorithm to approximate an optimal stopping of a time series that corresponds to a sequence of events is provided. The method includes: receiving information that relates to an event sequence; estimating, based on the received information, a first potential reward that is obtained by stopping the event sequence at a first time, and a set of respective second potential rewards that are obtained by stopping the event sequence at corresponding times; and determining, based on the estimated first and second potential rewards, an optimal time for stopping the event sequence. The event sequence may include a numerical sequence that is modeled as a statistical learning method via a Gaussian Process (GP) function and/or a deep GP function that indicates a probability density distribution of the items in the numerical sequence over a predetermined time interval.