Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

@article{Ishitani2013MathematicalFO,
  title={Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact},
  author={Kensuke Ishitani and Takashi Kato},
  journal={ERN: Optimization Techniques; Programming Models; Dynamic Analysis (Topic)},
  year={2013}
}
  • Kensuke Ishitani, Takashi Kato
  • Published 2013
  • Economics, Computer Science, Mathematics
  • ERN: Optimization Techniques; Programming Models; Dynamic Analysis (Topic)
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise part. Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control… Expand
An Optimal Execution Problem with S-shaped Market Impact Functions
In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on $[0,Expand
An Optimal Execution Problem with S-Shaped Market Impact Functions
In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on $[0,Expand
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 limitExpand

References

SHOWING 1-10 OF 38 REFERENCES
An optimal execution problem with market impact
  • Takashi Kato
  • Mathematics, Computer Science
  • Finance Stochastics
  • 2014
TLDR
It is found that right-continuity at the time origin is associated with the strength of market impact for large sales; otherwise the value function is continuous. Expand
Optimal Execution Under Jump Models For Uncertain Price Impact
In the execution cost problem, an investor wants to minimize the total expected cost and risk in the execution of a portfolio of risky assets to achieve desired positions. A major source of theExpand
Optimal control of execution costs
We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block SM of shares to beExpand
Dynamical Models of Market Impact and Algorithms for Order Execution
In this review article, we present recent work on the regularity of dynamical market impact models and their associated optimal order execution strategies. In particular, we address the question ofExpand
An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process
We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and showExpand
No-dynamic-arbitrage and market impact
Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationshipExpand
Optimal execution strategies in limit order books with general shape functions
TLDR
This work builds on the resilience model proposed by Obizhaeva and Wang (2005) but allows for a general shape of the LOB defined via a given density function, and obtains a new closed-form representation for the optimal strategy of a risk-neutral investor. Expand
VWAP execution as an optimal strategy
TLDR
This study explicitly introduces a trading volume process into the Almgren--Chriss model, which is a standard model for optimal execution and shows that the VWAP strategy is the optimal execution strategy for a risk-neutral trader. Expand
Large investor trading impacts on volatility
We begin with this paper a series devoted to a tentative model for the influence of hedging on the dynamics of an asset. We study here the case of a “large” investor and solve two problems in theExpand
Optimal execution of portfolio trans-actions
TLDR
This paper explicitly constructs the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty, and leads to the concept of Liquidity-adjusted VAR, or L-VaR, that explicitly considers the best tradeoff between volatility risk and liquidation costs. Expand
...
1
2
3
4
...