Lexicographic goal programming approach for portfolio optimization

This paper will investigate the optimum portfolio for an investor, taking into account 5 criteria. The mean variance model of portfolio optimization that was introduced by Markowitz includes two objective functions; these two criteria, risk and return do not encompass all of the information about investment; information like annual dividends, S P star ranking and return in later years which is estimated by using data from a longer history. Thus portfolio selection is a typical multi-objective decision making (MODM) problem. It is well known that Goal Programming (GP), based on preemptive priorities and target values, has been successful in solving MODM problems. In this paper we rank objectives of the MODM model according to weights elicited from Decision Maker’s (DM) preferences. Then we obtain goals from DM’s opinion. As a guidance for DM, we revise these goals consistent with ranking of objectives by a Linear Programming model in a way that new goals remain as close as possible to DM’s goals. After obtaining the goals we solve our MODM problem by a Lexicographic Goal Programming (LGP) model which is constructed by prioritizing objectives. Finally we illustrate our proposed LGP model by a numerical example.