Adaptive basket liquidation. (English) Zbl 1376.91156
This paper deals with the infinite-horizon optimal basket portfolio liquidation problem for a von Neumann-Morgenstern investor in a multi-asset extension of the liquidity model of Almgren with cross-asset impact. The author shows that a unique mean-variance optimal trading strategy exists and that it satisfies both Bellman’s principle of optimality and the Beltrami identity. It is shown that the mean-variance costs of liquidation fulfill the dynamic programming partial differential equation. Then it is constructed a solution to the HJB equation for utility maximization. The author constructs the utility maximization value function by solving two-dimensional partial differential equation. Using a verification argument it is shown that the solution to the HJB equation is indeed the value function. It is found that the set of portfolios that are held during the liquidation is independent of the investor’s utility function and only depends on the market volatility and liquidity structure. The utility function only influences how quickly the investor executes the trades. The partial differential equations for both the sequence of portfolios reached during the execution and the trading speed are derived.
Reviewer: Aleksandr D. Borisenko (Kyïv)
MSC:
| 91G10 | Portfolio theory |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35K65 | Degenerate parabolic equations |
Keywords:
optimal basket liquidation; von Neumann-Morgenstern investor; cross-asset impact; dynamic trading strategies; separation theoremReferences:
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