Related papers: Some Computations for Optimal Execution with Monot…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented…
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a…
We study optimal execution in markets with transient price impact in a competitive setting with $N$ traders. Motivated by prior negative results on the existence of pure Nash equilibria, we consider randomized strategies for the traders and…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk.…
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under…
We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share…
In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
This article provides a novel framework to evaluate limit order tactics that highlights expected fill price, adverse price selection cost, and opportunity cost. We formulate the problem of optimal execution of market orders with nonlinear…
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's…
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…
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
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,…
This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP)…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal…