# The Treasury

The Treasury serves as the backbone of our financial ecosystem, fortified by an array of computational models and strategies aimed at enhancing cash flow, liquidity, and overall asset management. This is particularly vital for ensuring long-term stability and profitability.



**Algorithms for Price Stability**

Key to our Treasury management are advanced algorithms that work cohesively to maintain the value and stability of our native token, LUCI. These algorithms automatically adjust supply parameters and collateral requirements based on current market conditions.



The Supply Adjustment Algorithm can be formulated as:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FpIyUfhN0DvCeKQKjMBaM%2Fimage.png?alt=media&#x26;token=85b5db47-997a-4af9-bb10-8b1efe3eaef8" alt=""><figcaption></figcaption></figure>

Where 𝛥S is the rate of supply adjustment.

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**Protocol-Owned Treasury Model**

Central to the Treasury's operation is the Protocol-Owned Treasury Model, which comprises various sources of funding, including but not limited to liquidations, minting, and partnerships.



The funding sources can be mathematically represented as:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2F6uBxmAthFCK37a8H6AY2%2Fimage.png?alt=media&#x26;token=f4bb7a55-c4f0-4e95-8534-e7afd58de961" alt=""><figcaption></figcaption></figure>

**Price Stabilization Mechanisms**

To ensure that the LUCI token maintains its value, we implement price stabilization mechanisms, especially during pivotal events like minting and burning. The Stabilization Ratio (SR) can be defined as:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FnRmUwtbidWTP4P6rO5vx%2Fimage.png?alt=media&#x26;token=d685f59d-2e4f-4ed6-98c1-aa46f46f10dd" alt=""><figcaption></figcaption></figure>

An SR value close to 1 indicates that the token is well-collateralized and stable.



**Liquidations and Price Oracle**

A grace period of 72 hours is set for liquidations when accounts reach a critical threshold, often related to the Minimum Collateralization Ratio (MCR). An algorithm monitors these parameters, triggering automated notifications to users.

The Price Oracle continually adjusts the value _P_ of assets and tokens based on market data.

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FFii1ADvNz6jERtYSLxKE%2Fimage.png?alt=media&#x26;token=d742dabd-f349-44c5-9a7b-0cf822cf89f5" alt=""><figcaption></figcaption></figure>

**Policy for Burning and Minting**

The treasury periodically mints new tokens as a method of funding. Minting can also occur when a borrower defaults. Let _M_ be the number of tokens minted, then:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FGRCrliM0M7DzpoHFiIPL%2Fimage.png?alt=media&#x26;token=0362835b-e7c9-4e64-9532-e48588f4ce8b" alt=""><figcaption></figcaption></figure>

Conversely, burning tokens occurs when a debtor clears their post-default debt. If _B_ is the number of tokens to be burned, it could be calculated as:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FJC5O6CeDrn1fJra2Gxjs%2Fimage.png?alt=media&#x26;token=61fbce7d-5f13-4248-8f13-4672933aa91d" alt=""><figcaption></figcaption></figure>

**Liquidity as a Service and AMMs**

To optimize returns, a portion _X_ treasury funds are allocated to liquidity providers and automated market makers (AMMs). This is often a fixed proportion α of the treasury's total available funds _T_.

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2Fps9EkDdW4H2KLNsC0kpx%2Fimage.png?alt=media&#x26;token=5e5ee891-2e3a-4b28-823e-538da2cb8778" alt=""><figcaption></figcaption></figure>

**Flash Loans and Arbitrage Bot**

The treasury employs an arbitrage bot that uses flash loans to seize arbitrage opportunities across decentralized exchanges. The profitability Π of this strategy can be estimated as:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2Fyl4nb1tSU658MImqWfLw%2Fimage.png?alt=media&#x26;token=b3b6b080-d91d-4153-8c40-0821fa304f61" alt=""><figcaption></figcaption></figure>

**Example**

Assume that the treasury has total available funds of 10,000 LUCI and wants to allocate 20% to liquidity providers and AMMs. In this case:

<figure><img src="https://2787681558-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FWQHokesx4twoLalR3b7N%2Fuploads%2FDmEMNmdLA95fyfgSaOyU%2Fimage.png?alt=media&#x26;token=b9b0d14e-7188-4378-a37b-1783027fe012" alt=""><figcaption></figcaption></figure>

This treasury model, coupled with an array of algorithms and external partnerships, aims to dynamically respond to market conditions and user behavior, safeguarding the ecosystem's stability and financial health.
