# A Generative Adversarial Network for Financial Advisor Recruitment in Smart Crowdsourcing Platforms
## 1 Introduction  
Modern Portfolio Theory (MPT) [1, 2, 3] or mean-variance analysis is a mathematical framework developed in 1952 by the Nobel Prize winning economist [PERSON] [4]. MPT is still a trending topic in research and several modern implementations of different approaches to solve this mathematical framework have been recently proposed in the literature [5, 6]. MPT studies the trade-off between the expected return of a portfolio and the level of market risk. For instance, it can be used to construct portfolios while maximizing their expected returns for a given risk level and likewise, reducing the market risk level for a desired portfolio's return value. MPT is mainly based on the concept of diversification underpinned by concepts of risk, return, variance, and covariance. Diversification [7, 8, 9, 10] is a key concept to reduce a portfolio's risk. For instance, the investment is diversified into multiple combinations of assets that are not perfectly and positively correlated. For example, U.S. Real Estate Investment Trusts (REITS) have a correlation to the S&P 500 of approximately 0.6, which means they are not highly correlated to the U.S. stock market, i.e., the price movement of one has no big impact on the price movement of the other and vice versa. For a given portfolio, the case of all perfectly positively correlations gives the highest possible standard deviation of portfolio return. In other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets. Diversification may also allow to obtain, for the same portfolio's expected return, a reduced risk. Therefore, with MPT, the focus is no longer on the return and the risk of an asset itselfbut it is on the asset's contribution to the overall risk and return of the portfolio [11; 12; 13; 14; 15; 16]. Moreover, MPT stipulates that all the investors are risk averse, i.e., the investors are more likely to choose portfolios with lower risk for a given expected return. Hence, reaching higher expected returns will require investors to accept more risk. In the literature, several studies addressed the challenge of portfolio optimization with different techniques. The authors of [17] considered a portfolio optimization model with real constraints which is commonly known as the Mean-Variance Cardinality Constrained Portfolio Optimization (MVCCPO) model and investigated two optimization algorithms to solve it, namely multi-objective covariance-based artificial bee colony, and e-new local search based multi-objective optimization algorithm. The investigated algorithms were tested on a large data set of assets and the obtained results were compared with the unconstrained efficient frontier of the corresponding data set. In [18], [PERSON] et al. considered a robust portfolio model based on the [PERSON] theory and turned it into a constrained Linear Matrix Inequalities (LMIs). Then, the authors employed the ellipsoid algorithm and interior-point method to solve it. To validate the results, the authors gave a numerical simulation in stock portfolio. In [19], the authors studied the problem of optimal portfolio diversification where they proposed a framework to help financial advisors determine the structure of optimal portfolio by mathematically modeling the dynamics of the markets and the stocks. In [20], the authors addressed the portfolio optimization challenge using the minimax principle. Their aim was to minimize an objective function defined as the maximum absolute deviation of all assets which represent the portfolio's risk. In [21], a deep reinforcement algorithm learning has been developed to construct portfolios and improve the trading strategy. The diversity of the proposed solutions in dealing with portfolio management suggests that each financial advisor has its own technique or strategy to address the Portfolio Optimization Problem (POP); hence, different financial portfolios are proposed to best respond to the investors' preferences and its targeted financial goals.