Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies
We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton--Jacobi--Bellman (HJB) partial differential equations (PDEs). In particular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic-variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the mean-variance strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian method results in significantly better accuracy than standard axis-aligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy.
Year of publication: |
2013
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Authors: | Tse ; Forsyth ; Kennedy ; Windcliff |
Published in: |
Applied Mathematical Finance. - Taylor & Francis Journals, ISSN 1350-486X. - Vol. 20.2013, 5, p. 415-449
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Publisher: |
Taylor & Francis Journals |
Saved in:
Online Resource
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