scholarly journals An FBSDE approach to market impact games with stochastic parameters

2021 ◽  
Vol 6 (3) ◽  
pp. 237
Author(s):  
Samuel Drapeau ◽  
Peng Luo ◽  
Alexander Schied ◽  
Dewen Xiong
Keyword(s):  
Nash Equilibrium ◽  
Unique Solution ◽  
Coupled System ◽  
Price Impact ◽  
Risk Averse ◽  
Impact Model ◽  
Market Impact ◽  
Stochastic Parameters ◽  
Unique Nash Equilibrium ◽  
Fully Coupled

<p style='text-indent:20px;'>In this study, we have analyzed a market impact game between <i>n</i> risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium. </p>

scholarly journals Nash Equilibrium for Risk-Averse Investors in a Market Impact Game with Transient Price Impact

2020 ◽  
pp. 2050001 ◽  
Author(s):  
Xiangge Luo ◽  
Alexander Schied
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Price Impact ◽  
Market Model ◽  
Risk Averse ◽  
Market Impact ◽  
Infinite Time ◽  
Time Horizons ◽  
Explicit Representations ◽  
Mean Variance

We consider a market impact game for [Formula: see text] risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential utility of their revenues. We give explicit representations for corresponding Nash equilibria and prove uniqueness in the case of mean-variance optimization. A qualitative analysis of these Nash equilibria is conducted by means of numerical analysis.

scholarly journals Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Astha Srivastava ◽  
Ankur Srivastava
Keyword(s):  
Nash Equilibrium ◽  
Economic Analysis ◽  
Standard Of Care ◽  
Limited Information ◽  
Liability Rule ◽  
Rule Based ◽  
Liability Rules ◽  
Levels Of Care ◽  
Unique Nash Equilibrium ◽  
Optimal Behaviour

AbstractIn accident law, we seek a liability rule that will induce both the parties to adopt socially optimal levels of precaution. Economic analysis, however, shows that none of the commonly used liability rules induce both parties to adopt optimal levels, if courts have access only to ‘Limited Information’ on. In such a case, it has also been established (K. (2006). Efficiency of liability rules: a reconsideration. J. Int. Trade Econ. Dev. 15: 359–373) that no liability rule based on cost justified untaken precaution as a standard of care can be efficient. In this paper, we describe a two-step liability rule: the rule of negligence with the defence of relative negligence. We prove that this rule has a unique Nash equilibrium at socially optimal levels of care for the non-cooperative game, and therefore induces both parties to adopt socially optimal behaviour even in case of limited information.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

2021 ◽  
Author(s):  
Muhammad Ejaz ◽  
Stephen Joe ◽  
Chaitanya Joshi
Keyword(s):  
Nash Equilibrium ◽  
Risk Analysis ◽  
Equilibrium Solution ◽  
Risk Averse ◽  
Prior Work ◽  
Reserve Price ◽  
Solution Concepts ◽  
Risk Seeking ◽  
Sealed Bid ◽  
Sealed Bid Auctions

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

COMMENTARY: Beyond the Black Box Revisited: Algorithmic Trading and TCA Analysis Using Excel

2018 ◽  
Keyword(s):  
Decision Process ◽  
Investment Decision ◽  
Black Box ◽  
Third Party ◽  
Algorithmic Trading ◽  
Impact Model ◽  
Market Impact ◽  
Proprietary Information ◽  
Analysis Techniques ◽  
Trading Decisions

In this paper we revisit techniques from “Creating Dynamic Pre-Trade Models: Beyond the Black Box” (Kissell, 2011) which was awarded The Journal of Trading’s Best Paper of the Year Award in 2011. We provide investors a pre-trade of pre-trade modeling technique that can be used to decipher broker and vendor models, and to calibrate a customized investor specific market impact model. We also provide a suite of Excel TCA Add-In functions that can incorporate investor specific market impact parameters and allow investors to perform TCA analysis on their own desktops within Excel, and with the added level of security and comfort that their investment decision process will not be reverse engineered because they do not need to upload or transmit any of their proprietary information and valuable trade information to a third-party website or API for analysis. Techniques in this paper enable investors to create their own customized TCA analyses within Excel to assist with both trading decisions and portfolio analysis and optimization.

scholarly journals Efficiency and Equilibrium in Network Games: An Experiment

2021 ◽  
pp. 1-44
Author(s):  
Edoardo Gallo ◽  
Chang Yan
Keyword(s):  
Nash Equilibrium ◽  
Network Structure ◽  
Economic Systems ◽  
Central Feature ◽  
Network Games ◽  
Trade Off ◽  
Network Game ◽  
Asymmetric Networks ◽  
Unique Nash Equilibrium

Abstract The tension between efficiency and equilibrium is a central feature of economic systems. We examine this trade-off in a network game with a unique Nash equilibrium in which agents can achieve a higher payoff by following a “collaborative norm”. Subjects establish and maintain a collaborative norm in the circle, but the norm weakens with the introduction of one hub connected to everyone in the wheel. In complex and asymmetric networks of 15 and 21 nodes, the norm disappears and subjects’ play converges to Nash. We provide evidence that subjects base their decisions on their degree, rather than the overall network structure.

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

2016 ◽  
Vol 32 (2) ◽  
pp. 207-219 ◽  
Author(s):  
Fande Kong ◽  
Xiao-Chuan Cai
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Coupled System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Krylov Method ◽  
Fine Mesh ◽  
Processor Cores ◽  
Fully Coupled

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

scholarly journals Slow Decay of Impact in Equity Markets

2015 ◽  
Vol 01 (02) ◽  
pp. 1550007 ◽  
Author(s):  
X. Brokmann ◽  
E. Sérié ◽  
J. Kockelkoren ◽  
J.-P. Bouchaud
Keyword(s):  
Power Law ◽  
Equity Markets ◽  
Impact Model ◽  
Market Impact ◽  
Temporal Dependence ◽  
Raw Data ◽  
Slow Decay ◽  
First Approximation ◽  
Information Contents ◽  
The Impact

Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a 10-day horizon in various equity markets. We find that the impact of single meta-orders is to a first approximation universal and slowly decays to zero (or to a small value), possibly as a power-law. We show that autocorrelated order-flows and trade information contents fully accounts for the apparent plateau observed in the raw data. We discuss the possible bias introduced by the quasi-linear assumption.

Applications to Economics

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Nash Equilibrium ◽  
Private Information ◽  
Price Competition ◽  
Quantal Response ◽  
Unique Nash Equilibrium ◽  
Common Effort ◽  
The Cost ◽  
All Pay Auction ◽  
Individual Effort ◽  
Applications To Economics

This chapter explores whether the equilibrium effects of noisy behavior can cause large deviations from standard predictions in economically relevant situations. It considers a simple price-competition game, which is also partly motivated by the possibility of changing a payoff parameter that has no effect on the unique Nash equilibrium, but which may be expected to affect quantal response equilibrium. In the minimum-effort coordination game studied, any common effort in the range of feasible effort levels is a Nash equilibrium, but one would expect that an increase in the cost of individual effort or an increase in the number of players who are trying to coordinate would reduce the effort levels observed in an experiment. The chapter presents an analysis of the logit equilibrium and rent dissipation for a rent-seeking contest that is modeled as an “all-pay auction.” The final two applications in this chapter deal with auctions with private information.

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