We consider the linear-impact case in the continuous-time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner's theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure-valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction-triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.

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International audienceThe viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies. By analyzing a model with linear instantaneous, transient, and permanent impact components, we discover a new class of irregularities, which we call transaction-triggered price manipulation strategies. We prove that price impact must decay as a convex nonincreasing function of time to exclude these market irregularities along with standard price manipulation. This result is based on a mathematical theorem on the positivity of minimizers of a quadratic form under a linear constraint, which is in turn related to the problem of excluding the existence of short sales in an optimal Markowitz portfolio

Chromosomal instability is a hallmark of cancer and correlates with the presence of extra centrosomes, which originate from centriole overduplication. Overduplicated centrioles lead to the formation of centriole rosettes, which mature into supernumerary centrosomes in the subsequent cell cycle. While extra centrosomes promote chromosome missegregation by clustering into pseudo-bipolar spindles, the contribution of centriole rosettes to chromosome missegregation is unknown. We used multi-modal imaging of cells with conditional centriole overduplication to show that mitotic rosettes in bipolar spindles frequently harbor unequal centriole numbers, leading to biased chromosome capture that favors binding to the prominent pole. This results in chromosome missegregation and aneuploidy. Rosette mitoses lead to viable offspring and significantly contribute to progeny production. We further show that centrosome abnormalities in primary human malignancies frequently consist of centriole rosettes. As asymmetric centriole rosettes generate mitotic errors that can be propagated, rosette mitoses are sufficient to cause chromosome missegregation in cancer.