UNDERLYING MATHEMATICAL AND STATISTICAL PRINCIPLES.pptx

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1. UNDERLYING MATHEMATICAL AND STATISTICAL PRINCIPLES

2. Algorithmic risk-based pricing is a form of dynamic pricing that uses advanced mathematical and statistical techniques to assess and quantify risk to set the optimal price for a product or service . It is used in finance, insurance, and retail to price loans, determine insurance premiums, and optimize retail prices based on demand and inventory

3. Foundational statistical principles Probability theory This is the basis for quantifying risk by modeling the likelihood of different outcomes.  Probability distributions:  Describe the likelihood of various outcomes. In finance, common distributions include the normal distribution for asset returns and the log-normal distribution for asset prices. Stochastic calculus:  Used for modeling the evolution of prices of risky assets over time, such as in the Black-Scholes model for option pricing. 

4. Statistical inference This allows models to make informed decisions and predictions based on data analysis. Hypothesis testing:  Assesses assumptions about market behavior or risk factors. For instance, testing if a certain factor significantly influences credit risk. Regression analysis : A standard method for modeling the relationship between a dependent variable (e.g., probability of default) and multiple independent variables (e.g., credit score, income). 

5. Core mathematical models and techniques Machine learning and AI Machine learning (ML) models are a key component of algorithmic pricing, using vast amounts of data to predict risk with higher accuracy than traditional methods.  Regression models : Used for supervised learning to predict continuous variables like a loan's interest rate based on borrower characteristics. Classification models : Techniques like logistic regression, random forests, and gradient-boosting machines can be used to predict the likelihood of an event, such as a loan default.  

6. Deep learning : Models such as Long Short-Term Memory (LSTM) networks are used for analyzing financial time series data, helping to forecast market volatility and manage risk. Explainable AI (XAI):  As ML models grow more complex, XAI techniques are used to interpret how a model arrives at its pricing decision, which is important for transparency and regulatory compliance

7. Optimization theory This is the mathematical framework for finding the best solution among all possible options. Portfolio optimization:  Models like the Markowitz portfolio theory use optimization to construct investment portfolios that maximize returns for a given level of risk. Pricing optimization:  Algorithms are designed to automatically set prices to achieve specific business objectives, such as maximizing profit or market share, based on various inputs. Kelly criterion : A formula used in algorithmic trading and risk management to determine the optimal size of a series of bets or investments to maximize long-term portfolio growth. 

8. Integration of principles for risk-based pricing These principles are combined to build a pricing algorithm through a process that includes:  Risk identification : Statistical and ML methods are used to identify potential risk factors, such as credit history, market trends, or borrower behavior. Data collection : Input data is collected from a variety of sources, including customer behavior, competitor prices, and macroeconomic indicators. Risk analysis:  Models, including ML and copulas, are trained on this data to quantify the likelihood and magnitude of potential negative outcomes.

9. Price determination : An optimization algorithm uses the risk analysis results, along with business rules and constraints, to set the price. The price is personalized or dynamically adjusted based on the assessed risk. Risk management : The process includes continuous monitoring, emergency stop systems, and controls on trade size and maximum drawdown to manage and mitigate various risks.