20 D. Barro and E. Canestrelli
follows
Pr(Wt≤zt)≤ 1 −θ Pr(WT≤zT)≤ 1 −θ
whereWtis the random variable representing the level of wealth. Under the as-
sumption of a discrete and finite number of realisations we can compute the shortfall
probability using the values of the wealth ineachnodeWkt=
∑n+ 1
i= 1 xikt.Thisgives
rise to a chance constrained stochastic optimisation problem which can be extremely
difficult to solve due to non-convexities which may arise, see [14].
5 Conclusions
We discuss the issue of including in the formulation of a dynamic portfolio optimisa-
tion problem both a minimum return guarantee and the maximisation of the potential
returns from a risky portfolio. To combine these two conflicting goals we formulate
them in the framework of a double dynamic tracking error problem using asymmetric
tracking measures.
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