Fuzzy Random λ‐Mean SAD Portfolio Selection Problem: An Ant Colony Optimization Approach

To reach the investment goal, one has to select a combination of securities among different portfolios containing large number of securities. Only the past records of each security do not guarantee the future return. As there are many uncertain factors which directly or indirectly influence the stock market and there are also some newer stock markets which do not have enough historical data, experts’ expectation and experience must be combined with the past records to generate an effective portfolio selection model. In this paper the return of security is assumed to be Fuzzy Random Variable Set (FRVS), where returns are set of random numbers which are in turn fuzzy numbers. A new λ‐Mean Semi Absolute Deviation (λ‐MSAD) portfolio selection model is developed. The subjective opinions of the investors to the rate of returns of each security are taken into consideration by introducing a pessimistic‐optimistic parameter vector λ. λ‐Mean Semi Absolute Deviation (λ‐MSAD) model is preferred as it follows absolute deviation of the rate of returns of a portfolio instead of the variance as the measure of the risk. As this model can be reduced to Linear Programming Problem (LPP) it can be solved much faster than quadratic programming problems. Ant Colony Optimization (ACO) is used for solving the portfolio selection problem. ACO is a paradigm for designing meta‐heuristic algorithms for combinatorial optimization problem. Data from BSE is used for illustration.