# ⚛️5. Mathematics

In this section, we explore additional mathematical concepts that can be applied to enhance the analysis of the objective function of the new economic system.

The objective function, as defined earlier:

$Success: MaxV = δ Digital Assets / δ Time$

This function is revolutionary, yet reductive. It does not explore the complex mathematics “systems” that must be applied to enhance this optimization problem, thereby enabling Elevated Artificial Intelligence “Elevated” - the “deep tech” of this company - to fully leverage its potential for optimized digital economy, for every individual. This section introduces additional mathematical tools and techniques that can be used to address complex challenges in the digital asset investment space.

The efficient market hypothesis (EMH) is a fundamental concept in finance that suggests that markets are “informationally efficient,” meaning that asset prices reflect all available information. This hypothesis has significant implications for investors and financial professionals, as it suggests that it is difficult to outperform the market consistently over time by using fundamental or technical analysis.

The EMH is typically broken down into three forms: weak, semi-strong, and strong. Weak form efficiency suggests that prices reflect all historical price and volume data. Semi-strong form efficiency suggests that prices reflect all publicly available information. Strong form efficiency suggests that prices reflect all information, including insider information.

The rise of digital assets and fungible tokens has led to new challenges in assessing the efficiency of capital markets. Digital assets are often subject to high levels of volatility and uncertain liquidity, and the lack of centralized regulation and oversight can lead to significant regulatory and security risks. In addition, due to the nature of these markets - fraught with inefficiencies and technological risk - it is abundantly clear that the EMH does not hold.

To address these challenges, among others, we propose a new mathematical model for assessing the efficiency of digital asset markets and constructing optimized portfolios of digital assets. Our model builds on the traditional EMH framework and incorporates additional penalty terms that account for illiquidity risk, transaction costs, regulatory risk, security risk, and network risk.

We define an objective function for financial success in the age of digital transformation that maximizes expected return subject to investor/user risk tolerance and other relevant factors. The resulting optimization problem can be solved using techniques from portfolio theory, such as Markowitz optimization, to select a set of digital assets that maximize expected return while minimizing risk.

Our framework has significant implications for investors operating in the digital asset space. We believe that its application (Elevated) will thereby legitimize consumer usability of DeFi, enabling the mass adoption of the new financial system. By incorporating penalty terms that account for the new or renewed complexities of this system, our framework enables investors to construct portfolios of digital assets that are better aligned with their risk tolerance and investment objectives.

Through the application of these models within a user-owned wallet, complete with superior UI/UX, the goal of Elevated is to democratize this supreme functionality for the masses, and result in unprecedented wealth generation for the ordinary individuals who adopt our product. As the digital asset space continues to evolve, we believe that our framework - Elevated AI - will become an increasingly valuable tool for any individual or professional/institution looking to adopt and navigate this complex and rapidly evolving landscape.

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