Pareto eficient buy and hold investment strategies under order book linked constraints

Abstract

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and "level II order book data", i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of "golden strategies", i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.