**6. References**


**Part 7** 

**Extended Applications of PID** 


**Part 7** 

**Extended Applications of PID** 

228 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

[8] L. Debnath, "A brief historical introduction to fractional calculus," Int. J. Math. Educ. Sci.

[9] Y. Q. Chen, D. Xue and H. Dou, "Fractional Calculus and Biomimetic Control," Proc. of

[10] D. Valrio, "Fractional Robust System Control," PhD thesis, Instituto Superior Tcnico,

[11] TSENG, Chien-Cheng ,''Design of fractional order digital FIR differentiators''. IEEE

[12] Concepcion Alicia Monje Micharet. ''Design Methods of Fractional Order Controllers

[13] Youxin Luo, Jianying Li, "The Controlling Parameters Tuning and its Application of

[14] Tehrani, K.A. Amirahmadi, A. Rafiei, S.M.R. Griva, G. Barrandon, L. Hamzaoui, M.

the First IEEE Int. Conf. on Robotics and Biomimet- ics (RoBio04), pp. robio2004-

for Industrial Applications''. Ph.D. thesis, University of Extremadura, Spain,

Fractional Order PID Bacterial Foraging-based Oriented by Particle Swarm Optimization" IEEE International Conference on Intelligent Computing and

Rasoanarivo, I. Sargos, F.M.,'' Design of fractional order PID controller for boost converter based on Multi-Objective optimization'', Power Electronics and Motion Control Conference (EPE/PEMC), 2010 14th International, Ohrid 6-8 Sept. 2010,pp:

Technol., vol. 35, no. 4,pp. 487-501, 2004.

Universidade Tcnica de Lisboa, 2005.

Intelligent Systems, 2009, pp. 4-7.

signal processing letters. 8:3 (2001) 77-79.

347, August 2004.

2006.

179-185.

**10** 

**via PID Control** 

*1University of Parma* 

*2M.I.T.* 

*1,3Italy 2USA* 

**An Innovative Systematic Approach to** 

Gino Gandolfi1, Antonella Sabatini1,2 and Monica Rossolini3

Portfolio management is the art and science of modifying the asset allocation of a financial portfolio in response to and/or in anticipation of market conditions and dynamics of financial markets. The modification of the asset allocation is obtained by rebalancing and varying the relative weights of the assets comprising the portfolio on a periodic basis. The asset manager considers two distinct portfolios: the financial portfolio subject to his management technique (referred to here as the experimental portfolio, or Portfolio "A"), and a benchmark (or comparison) portfolio called Portfolio "B". The asset manager composes his experimental portfolio, also referred to as the benchmark-based portfolio, following, generally, two different types of strategies: active and passive (indexed) strategy. In this work, we analyze a fundamental aspect of portfolio management: the active asset allocation. The objective of this writing is to illustrate a new asset allocation technique to compose an experimental portfolio, which uses the Proportional, Integral, Derivative (PID) controller aiming to overcome a benchmarked portfolio. Therefore, the two portfolios taken into consideration are the experimental portfolio subject to the PID controlling methodology and a buy-and-hold diversified portfolio as the benchmark portfolio. The technique consists in managing portfolio asset-allocation revisions through PID control, a tool that is highly utilized and implemented in the engineering, industrial processing units and in production plants. The goal is to achieve a good portfolio performance trying to control volatility; in other words, the goal is to obtain good performance of risk adjusted returns. Thus, in finance, financial market assets forming a portfolio or a market benchmark represent the

A brief literature review covering the comparison between strategic and tactical asset allocation introduces the topic, followed by some examples of tactical asset allocation techniques. Subsequently, this article illustrates how the PID controller functions. Then, it exemplifies the new asset allocation technique, functioning, and methodology. This work shows how a portfolio managed by this new technique attains fine results of risk adjusted

**1. Introduction** 

process plant controlled by the PID controller.

returns compared with a benchmark.

*3"Banking and Finance" Tor Vergata University, SDA Bocconi* 

**Financial Portfolio Management** 
