The investor wants to invest his money in objects of great value often referred to as assets. Examples of assets include stocks, bonds or company shares. A collection of assets which the investor invests in is referred to as a portfolio In general, the investors ask for financial analysts' help in finding the best assets to invest in that have acceptable risk with profitable return. The investor prefers investing into multiple assets instead of one to divide his budget on multiple assets so that if some assets' values increase while others' values drop, then the combined risk is low, so by that the investor would be minimizing risk as much as possible.
Although some investors rely on instincts and observations to compose an efficient portfolio, an approach can be suggested to calculate the expected returns and the minimum risk, and to take into consideration a magnitude of parameters and constraints.
Models are used to provide an abstract / mathematical representation of this process. One of these models is the Mean Variance model. In this MV Model, the expected return is the mean from the assets and the risk is the variance from the assets. Calculating the return and the risk helps determine if a certain number of assets are of great value for future investment. Portfolio Optimization is also considered to be the foundation for selecting the asset to invest to. This is considered to be the aim for portfolio optimization since what is required is selecting the assets that can offer the investor highest profit and minimum risk. There should always be a risk tolerance assigned to the problem which corresponds to the maximal risk an investor can tolerate during which he requires to maximize the return. Therefore a trade-off between return and risk is always required.
Markowitz was the first to define the mean-variance model (MV) which is part of the modern portfolio theory. This model is quadratic, which can be solved by math programming methods. The model depends on trying to maximize the returns for a given risk. The result of these sets of portfolios will be a Pareto (Reference Needed) frontier having for each particular portfolio no other one with equal return and lesser risk, and no other one with equal risk and greater return. Therefore, a heuristic or meta-heuristic approach is needed. The motivation for this is to try new meta-heuristics to the problem which saves run time and gives equal or better solutions than existing methods in literature.
Talking about the complexity, the Portfolio Optimization problem is considered to be an NP-Complete problem which is in the set of NP problems and it belongs to NP-Hard problems category. By definition, NP problems are the set of problems such that their solutions are verified in polynomial time. Concerning the NP-Hard problem, a problem X is considered to be NP-Hard if and only if there is an NP-Complete problem Y that is polynomial time reducible to X.
Several algorithms have been used to solve the Portfolio Optimization problem, which are summarized in Chapter 3 ' Literature Review. In this thesis, we design a Cuckoo Search algorithm for providing good suboptimal solutions. In the recent decades, we noticed a huge research on nature motivated algorithms and we can mention few algorithms like Evolutionary Computing, Neural Networks and Swarm Optimization. In our thesis, the nature base algorithm that we are going to tackle is Cuckoo Search. This algorithm was inspired from the nature and more specifically because of a bird type called Cuckoo.
Cuckoo Search is an Optimization Population Based Algorithm. It was invented and developed by Xin-She Yang and Suash Deb in 2009. They discovered that the Random-Walk style search is better performed by L??vy flights, which is the concept of mutating and searching between one nest to another for better solution, rather than simple random walk.
We evaluated our Cuckoo Search algorithm by using real world / published data sets. Our experimental results showed comparable and better results compared to Particle Swarm Optimization and Tabu Search.
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