💰Mathematical Model of AI-Driven Liquidity Mining Logic
To comprehensively express the logic of the AI autonomous decision-making layer and computational power layer of the TCASH public chain in areas such as multi-chain mapping, liquidity mining, and risk control, an integrated mathematical model can be constructed. This model will encompass core elements such as AI decision-making, cross-chain mapping, yield optimization, and risk management.
Core Model
1. Definition of Symbols and Variables
Blockchain Set
• C={C₁,C₂,...,Cn}: The set of supported public blockchains, such as Ethereum, TRON, BNB Smart Chain, etc.
Native Currency and Token Set
• For each blockchainc∈C:
• Mc: The native currency of blockchain(e.g., ETH for Ethereum).
• Tc={tc₁,tc₂,..}: The set of tokens on blockchain c that support POS mining.
Yield Pool and Staking Pair
• Pc={Pc₁,Pc₂,…}: The set of staking pairs on blockchain, where each staking pair Pₐᵢ consists of a native currency and a token, such as (Mc,tcj)。
Investment Duration Set
• D={d₁,d₂,d₃}={24h,48h,72h}: The set of available investment durations.
Investment Amount and Allocation
• A: Total investment amount.
• We,p,d: The amount of investment allocated to staking pair on blockchain for duration
Yield and Risk Functions
• Rc,p,d: The expected annual percentage rate (APR) for staking pair over duration .
• Vc,p: The risk assessment value for staking pair .
AI Decision-Making Function
• AI: The AI model used to optimize the investment portfolio, maximizing returns while keeping risks manageable.
2. Objective Function and Constraints
• Objective Function (Maximize Expected Returns)
• Total Investment Amount Constraint
• Risk Control Constraint
Where 𝑉 max is the maximum acceptable risk value set by the AI model.
• Non-Negative Investment Constraint
Wc,p,d≥0,Vc∈C,Vp∈Pc,Vd∈D
3. Optimization Process of the AI Model
1.Yield Prediction: The AI model utilizes deep learning to predict the expected yield rate for each staking pair.
• Rc,p,d= Yield: (Historical yield data, market trends, liquidity, transaction volume)
2.Risk Assessment:
The AI model evaluates the risk of each staking pair.
• Vc,p= Risk: (Price volatility, market depth, project reputation, security audit results, social media sentiment)
3.Optimization Algorithm:
The AI model solves the objective function to determine the optimal investment portfolio.
{we,pa}: {wc,p,d}=AI(max E[Rtotal],subject to constraints)
This often involves solving an optimization problem with linear or nonlinear constraints, utilizing methods such as gradient descent, genetic algorithms, or other advanced optimization techniques.
4. Time Dimension and Dynamic Adjustment
1.Time Discretization：
Time is divided into discrete periods, such as hourly or daily, denoted as t =1,2,...,T
2.Dynamic Adjustment Strategy:
In each time period t , the AI model updates yield and risk assessments based on the latest data and adjusts the investment portfolio accordingly.
5. Risk Control and Fault Tolerance Mechanism
1.Risk Reserve Mechanism：
A risk reserve fund , is established for each staking pair to address potential losses：
Where is the risk reserve ratio coefficient.
2.Fault Tolerance Handling：
When the AI model predicts anomalies or risks exceeding the threshold, the fault tolerance mechanism is triggered:
● Suspend New Investments: Halt new investments in high-risk staking pairs.
● Closing Positions: Gradually withdraw existing investments to reduce risk exposure.
● Strategy Adjustment: Reevaluate the investment strategy and update the risk assessment model.
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