📐Mathematical Modeling

The AI’s functionalities are supported by various mathematical models:

Cross-Chain Swap Optimization

The optimization problem for selecting the most efficient path for cross-chain swaps can be modeled as a shortest-path problem:

$$\min_{p \in P} \sum_{i=1}^{n} c(p_i)$$

Where:

𝑝 is the path selected for the transaction.

𝐶(𝑝𝑖) is the cost associated with the 𝑖-th segment of the path, including gas fees, latency, and liquidity constraints.

Portfolio Optimization

Portfolio optimization is modeled as a mean-variance optimization problem:

$$\min_{w} \left\{ -\mu^T w + \frac{\lambda}{2} w^T \sum w \right\}$$

Where:

𝑤 is the vector of portfolio weights.

𝜇 is the expected return vector.

Σ is the covariance matrix of asset returns.

λ is the risk aversion parameter.

Transaction Cost Estimation

The cost of executing a transaction is estimated using a linear regression model:

$$\text{Estimated Cost} = \alpha + \beta_1 \times \text{Gas Price} + \beta_2 \times \text{Network Congestion} + \epsilon$$

Where:

𝛼,𝛽1,𝑎𝑛𝑑 𝛽2 are coefficients estimated from historical data.

ϵ represents the error term.

Tax Liability Calculation

The tax liability for capital gains is calculated as:

\text{Tax Liability} = \sum_{i=1}^{n} \text{Tax Rate} \times (\text{Sell Price}_i - \text{Buy Price}_i) \times \text{Holding Period Adjustment} \

Where:

Tax Rate is determined by the jurisdiction’s rules.

Sell Price and Buy Price are the prices at which the cryptocurrency was sold and bought, respectively.

Holding Period Adjustment accounts for differences in tax rates for short-term vs. long-term capital gains.