Optimal dynamic asset allocation in a non–Gaussian world 2814 Conclusions
In this paper we considered the Optimal Dynamic Asset Allocation problem. Given
a sequence of target sets that the investor would like his portfolio to stay within, the
optimal strategy is synthesised in order to maximise the joint probability of fulfilling
the investment requirements. The approach does not assume any specific distributions
for the asset classes’ stochastic dynamics, thus being particularly appealing to treat
non-Gaussian asset classes. The proposed optimal control problem has been solved by
leveraging results on stochastic invariance. The optimal solution exhibits a contrarian
attitude, thus performing very well in oscillating markets.
Acknowledgement.The author would like to thank Giordano Pola (University of L’Aquila,
Center of Excellence DEWS, Italy), Roberto Dopudi and Sylvie de Laguiche (Cr ́edit Agricole
Asset Management) for stimulating discussions on the topic of this paper.
Appendix: Markets MMGM modeling
Asset classes used in the case study present significant deviation to gaussianity. This
market scenario has been modelled by a 2-state MMGM. States 1 and 2 are charac-
terised by the following univariate statistics:^5
{μ 1 (i)}i=[0. 000611 ; 0. 001373 ; 0 .002340],
{σ 1 (i)}i=[0. 000069 ; 0. 005666 ; 0 .019121],
{μ 2 (i)}i=[0. 000683 ;− 0. 016109 ;− 0 .017507],
{σ 2 (i)}i=[0. 000062 ; 0. 006168 ; 0 .052513],and correlation matrix:^6
CB E
corr to C 1 0. 0633 0. 0207
corr to B 0. 0633 1 − 0. 0236
corr to E 0. 0207 − 0. 0236 1Transition probabilities are uniform and the unconditional probability of State 1 is
98%. The above MMGM model correctly represents the univariate statistics of the
asset classes up to the fourth order (as detailed in Table 1) and up to the second order
concerning the correlation patterns.
(^5) μs(i)andσs(i)indicate (resp.) the performance and volatility of assetiin the states.(Values
are weekly based.)
(^6) We assume the same correlation matrix for the above gaussian models.