Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

The LIM-only protein FHL2 attenuates lung inflammation during bleomycin-induces fibrosis

Fibrogenesis is usually initiated when regenerative processes have failed and/or chronic inflammation occurs. It is characterised by the activation of tissue fibroblasts and dysregulated synthesis of extracellular matrix proteins. FHL2 (four-and-a-half LIM domain protein 2) is a scaffolding protein that interacts with numerous cellular proteins, regulating signalling cascades and gene transcription. It is involved in tissue remodelling and tumour progression. Recent data suggest that FHL2 might support fibrogenesis by maintaining the transcriptional expression of alpha smooth muscle actin and the excessive synthesis and assembly of matrix proteins in activated fibroblasts. Here, we present evidence that FHL2 does not promote bleomycin-induced lung fibrosis, but rather suppresses this process by attenuating lung inflammation. Loss of FHL2 results in increased expression of the pro-inflammatory matrix protein tenascin C and downregulation of the macrophage activating C-type lectin receptor DC-SIGN. Consequently, FHL2 knockout mice developed a severe and long-lasting lung pathology following bleomycin administration due to enhanced expression of tenascin C and impaired activation of inflammation-resolving macrophages

Calibration of optimal execution of financial transactions in the presence of transient market impact

Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate with real data the optimal execution problem both for risk neutral and for risk averse investors and we derive an efficient frontier of optimal execution. When we include spread costs the problem must be solved numerically and we show that the introduction of such costs regularizes the solution.Comment: 31 pages, 8 figure

An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014