Description
1st talk
Speaker: Peter Bank, TU Berlin
Title: Optimal execution and speculation with trade signals
Abstract: We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$\sigma$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. Her trades impact the market through the same mechanism as other orders. A novel version of Marcus-type SDEs allows us to efficiently describe the intricate timing of market dynamics at moments when her orders concur with others. In this setting, we examine an optimal execution problem and derive the Hamilton--Jacobi--Bellman (HJB) equation for the value function. The HJB equation is solved numerically and we illustrate how the trader uses the signal to enhance the performance of execution problems and to execute speculative strategies. This is joint work with Alvaro Cartea and Laura Körber.
2nd talk
Speaker: Yan Dolinsky, Hebrew University, Jerusalem
Title: Some Computations for Optimal Execution with Monotone Strategies
Abstract: We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the number of shares and the selling rate are non-negative processes. For this case we give a complete characterization of the value and the optimal control via a solution of a non-linear ordinary differential equation (ODE). Furthermore, we provide an example where the non-linear ODE can be solved explicitly. Our approach is purely probabilistic.
3rd talk
Speaker: Miklós Rásonyi, Rényi Institute, Budapest
Title: Utility maximization in markets with transient price impact
Abstract:
We consider a discrete-time model of a financial market with transient price impact, following earlier work by P. Bank and Y. Dolinsky. We point out that, surprisingly, the set of attainable wealth may fail to be convex. Despite this difficulty, we show the existence of an optimal strategy for a utility maximizer, without additional assumptions that were present in past papers. Based on joint work with Lorant Nagy.