Piecewise Nonlinear Goal-directed Portfolio Insurance Strategies under TIPP Idea

Traditional portfolio insurance (PI) strategy, such as CPPI, only considers the floor constraint but not the goal aspect. This paper proposes a goal-directed (GD) strategy to express an investor’s goal-directed trading behavior and combines this floor-less GD strategy with the goal-less CPPI strategy to form a piecewise linear goal-directed CPPI (GDCPPI) strategy. In addition, we extend the piecewise linear GDCPPI strategy to be a piecewise nonlinear GDCPPI strategy. Furthermore, we replace CPPI concept by TIPP idea to generate related GDTIPP strategies. The piecewise GDCPPI and GDTIPP strategies are special cases of goaldirected portfolio insurance (GDPI) strategy. This paper applies genetic algorithm (GA) technique to find better piecewise linear GDPI strategy parameters than those under the Brownian motion assumption. This paper also applies forest genetic programming (GP) technique to generate the piecewise nonlinear GDPI strategy. The statistical tests show that the GP strategy outperforms the GA strategy which in turn outperforms the Brownian strategy.