We analyze a controlled price formation experiment in the laboratory that
shows evidence for bubbles. We calibrate two models that demonstrate with high
statistical significance that these laboratory bubbles have a tendency to grow
faster than exponential due to positive feedback. We show that the positive
feedback operates by traders continuously upgrading their over-optimistic
expectations of future returns based on past prices rather than on realized
returns.

This paper focuses on an extension of the Limit Order Book (LOB) model with
general shape introduced by Alfonsi, Fruth and Schied. Here, the additional
feature allows a time-varying LOB depth. We solve the optimal execution problem
in this framework for both discrete and continuous time strategies. This gives
in particular sufficient conditions to exclude Price Manipulations in the sense
of Huberman and Stanzl or Transaction-Triggered Price Manipulations (see
Alfonsi, Schied and Slynko).

We give a complete solution to the problem of minimizing the expected
liquidity costs in presence of a general drift when the underlying market
impact model has linear transient price impact with exponential resilience. It
turns out that this problem is well-posed only if the drift is absolutely
continuous. Optimal strategies often do not exist, and when they do, they
depend strongly on the derivative of the drift.

A limit order book provides information on available limit order prices and
their volumes. Based on these quantities, we give an empirical result on the
relationship between the bid-ask liquidity balance and trade sign and we show
that liquidity balance on best bid/best ask is quite informative for predicting
the future market order's direction. Moreover, we define price jump as a sell
(buy) market order arrival which is executed at a price which is smaller
(larger) than the best bid (best ask) price at the moment just after the
precedent market order arrival.

We propose a model for the dynamics of a limit order book in a liquid market
where buy and sell orders are submitted at high frequency. We derive a
functional central limit theorem for the joint dynamics of the bid and ask
queues and show that, when the frequency of order arrivals is large, the
intraday dynamics of the limit order book may be approximated by a Markovian
jump-diffusion process in the positive orthant, whose characteristics are
explicitly described in terms of the statistical properties of the underlying
order flow.

We demonstrate that a stochastic model consistent with the scaling properties
of financial assets is able to replicate the empirical statistical properties
of the S&P 500 high frequency data within a window of three hours in each
trading day. This result extends previous findings obtained for EUR/USD
exchange rates. We apply the forecast capabilities of the model to implement an
explicit trading strategy. Trading signals are model-based and not derived from
chartist criteria.

We consider an illiquid financial market where a risk-averse investor has to
liquidate a large portfolio within a finite time horizon [0,T] and can trade
continuously at a traditional exchange (the "primary venue") and in a dark
pool. At the primary venue, trading yields a linear price impact. In the dark
pool, no price impact costs arise but order execution is uncertain, modeled by
a multi-dimensional Poisson process.

We introduce a prototype model in an attempt to capture some aspects of
market dynamics simulating a trading mechanism. The model description starts
with a discrete-space, continuous-time Markov process describing arrival and
movement of orders with different prices. We then perform a re-scaling
procedure leading to a deterministic dynamical system controlled by non-linear
ordinary differential equations (ODEs). This allows us to introduce
approximations for the equilibrium distribution of the model represented by
fixed points of deterministic dynamics.

Asset liquidity in modern financial markets is a key but elusive concept. A
market is often said to be liquid when the prevailing structure of transactions
provides a prompt and secure link between the demand and supply of assets, thus
delivering low costs of transaction. Providing a rigorous and empirically
relevant definition of market liquidity has, however, provided to be a
difficult task. This paper provides a critical review of the frameworks
currently available for modelling and estimating the market liquidity of
assets.

We define a numerical method that provides a non-parametric estimation of the
kernel shape in symmetric multivariate Hawkes processes. This method relies on
second order statistical properties of Hawkes processes that relate the
covariance matrix of the process to the kernel matrix. The square root of the
correlation function is computed using a minimal phase recovering method. We
illustrate our method on some examples and provide an empirical study of the
estimation errors. Within this framework, we analyze high frequency financial
price data modeled as 1D or 2D Hawkes processes.

We propose a flexible framework for profit-seeking market making by combining
cost function based automated market makers with bandit learning algorithms.
The key idea is to consider each parametrisation of the cost function as a
bandit arm, and the minimum expected profits from trades executed during a
period as the rewards. This allows for the creation of market makers that can
adjust liquidity and bid-asks spreads dynamically to maximise profits.

We consider the optimal trade execution strategies for a large portfolio of
single stocks proposed by Almgren (2003). This framework accounts for a
nonlinear impact of trades on average market prices. The results of Almgren
(2003) are based on the assumption that no shares of assets per unit of time
are trade at the beginning of the period. We propose a general solution method
that accomodates the case of a positive stock of assets in the initial period.
Our findings are twofold.

The asymmetric price impact between the institutional purchases and sales of
32 liquid stocks in Chinese stock markets in year 2003 is carefully studied. We
analyze the price impact in both drawup and drawdown trends with consecutive
positive and negative daily price changes, and test the dependence of the price
impact asymmetry on the market condition. For most of the stocks institutional
sales have a larger price impact than institutional purchases, and larger
impact of institutional purchases only exists in few stocks with primarily
increasing tendencies.

In financial markets, abnormal trading behaviors pose a serious challenge to
market surveillance and risk management. What is worse, there is an increasing
emergence of abnormal trading events that some experienced traders constitute a
collusive clique and collaborate to manipulate some instruments, thus mislead
other investors by applying similar trading behaviors for maximizing their
personal benefits.

In this paper we apply a new approach of the string theory to the real
financial market. The strings are defined here by the boundary conditions,
characteristic length, real values and the method of redistribution of
information. The map represents the detrending and data standardization
procedure. We used 1-end-point, 2-end-point open string and partially
compactified strings that satisfy the Dirichlet and Neumann boundary
conditions. We established two different models to predict the behavior of
financial forex market.

Equity order flow is persistent in the sense that buy orders tend to be
followed by buy orders and sell orders tend to be followed by sell orders. For
equity order flow this persistence is extremely long-ranged, with positive
correlations spanning thousands of orders, over time intervals of up to several
days. Such persistence in supply and demand is economically important because
it influences the market impact as a function of both time and size and because
it indicates that the market is in a sense out of equilibrium.

We consider idealized financial markets in which price paths of the traded
securities are cadlag functions, imposing mild restrictions on the allowed size
of jumps. We prove the existence of quadratic variation for typical price
paths, where the qualification "typical" means that there is a trading strategy
that risks only one monetary unit and brings infinite capital if quadratic
variation does not exist. This result allows one to apply numerous known
results in pathwise Ito calculus to typical price paths; we give a brief
overview of such results.

We study an optimal execution problem in a market model which considers
market impact. First we study a discrete-time model and describe a value
function. Then, by shortening the intervals of the execution times, we derive
the value function of a continuous-time model and study some of its properties
(continuity, semi-group property and viscosity property). We show that these
vary with the strength of the market impact. We introduce some examples which
show that the forms of the optimal strategies change completely, depending on
the amount of the trader's security holdings.

In this paper the problem of optimal derivative design, profit maximization
and risk minimization under adverse selection when multiple agencies compete
for the business of a continuum of heterogenous agents is studied. The presence
of ties in the agents' best-response correspondences yields discontinuous
payoff functions for the agencies. These discontinuities are dealt with via
efficient tie--breaking rules.

We propose a framework for studying optimal market making policies in a limit
order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain
with finite values, multiple of the tick size, and subordinated by the Poisson
process of the tick-time clock. We consider a small agent who continuously
submits limit buy/sell orders and submits market orders at discrete dates. The
objective of the market maker is to maximize her expected utility from revenue
over a short term horizon by a tradeoff between limit and market orders, while
controlling her inventory position.

As demonstrated during the recent financial crisis, regulators require
additional analytical tools to assess systemic risk in the financial sector.
This paper describes one such tool; namely a novel market modeling and analysis
capability. Our model builds upon two leading market models: one which
emphasizes market micro-structure and another which emphasizes an ecology of
trading strategies. We address a limitation of market modeling, namely the
consideration of only one dominant trading strategy (i.e., long positions).

In this paper, we present a multi-period trading model by assuming that
traders face not only asymmetric information but also heterogenous prior
beliefs, under the requirement that the insider publicly disclose his stock
trades after the fact. We show that there is an equilibrium in which the
irrational insider camouflages his trades with a noise component so that his
private information is revealed slowly and linearly whenever he is
overconfident or underconfident.

We propose a dynamical theory of market liquidity that predicts that the
average supply/demand profile is V-shaped and {\it vanishes} around the current
price. This result is generic, and only relies on mild assumptions about the
order flow and on the fact that prices are (to a first approximation)
diffusive. This naturally accounts for two striking stylized facts: first,
large metaorders have to be fragmented in order to be digested by the liquidity
funnel, leading to long-memory in the sign of the order flow.

We propose and study a simple stochastic model for the dynamics of a limit
order book, in which arrivals of market order, limit orders and order
cancellations are described in terms of a Markovian queueing system. Through
its analytical tractability, the model allows to obtain analytical expressions
for various quantities of interest such as the distribution of the duration
between price changes, the distribution and autocorrelation of price changes,
and the probability of an upward move in the price, {\it conditional} on the
state of the order book.

This paper examines the intra-day seasonality of transacted limit and market
orders in the DEM/USD foreign exchange market. Empirical analysis of completed
transactions data based on the Dealing 2000-2 electronic inter-dealer broking
system indicates significant evidence of intraday seasonality in returns and
return volatilities under usual market conditions. Moreover, analysis of
realised tail outcomes supports seasonality for extraordinary market conditions
across the trading day.

We study a single risky financial asset model subject to price impact and
transaction cost over an finite time horizon. An investor needs to execute a
long position in the asset affecting the price of the asset and possibly
incurring in fixed transaction cost. The objective is to maximize the
discounted revenue obtained by this transaction. This problem is formulated as
an impulse control problem and we characterize the value function using the
viscosity solutions framework.

Buying or selling assets leads to transaction costs for the investor. On one
hand, it is well know to all market practionaires that the transaction costs
are positive on average and present therefore systematic loss. On the other
hand, for every trade, there is a buy side and a sell side, the total amount of
asset and the total amount of cash is conserved. I show, that the apparently
paradoxical observation of systematic loss of all participants is intrinsic to
the trading process since it corresponds to a correlation of outstanding orders
and price changes.

In this paper, we present a multi-period trading model in the style of Kyle
(1985)'s inside trading model, by assuming that there are at least two insiders
in the market with long-lived private information, under the requirement that
each insider publicly discloses his stock trades after the fact. Based on this
model, we study the influences of "public disclosure" and "competition among
insiders" on the trading behaviors of insiders.

We study a variation of the minority game. There are N agents. Each has to
choose between one of two alternatives everyday, and there is reward to each
member of the smaller group. The agents cannot communicate with each other, but
try to guess the choice others will make, based only the past history of number
of people choosing the two alternatives. We describe a simple probabilistic
strategy using which the agents acting independently, can still maximize the
average number of people benefitting every day.

We introduce a new stochastic model for the variations of asset prices at the
tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of
assets). The construction is based on marked point processes and relies on
linear self and mutually exciting stochastic intensities as introduced by
Hawkes. We associate a counting process with the positive and negative jumps of
an asset price. By coupling suitably the stochastic intensities of upward and
downward changes of prices for several assets simultaneously, we can reproduce
microstructure noise (i.e.

Kyle (1985) builds a pioneering and influential model, in which an insider
with long-lived private information submits an optimal order in each period
given the market maker's pricing rule. An inconsistency exists to some extent
in the sense that the ``constant pricing rule " actually assumes an adaptive
expected price with pricing rule given before insider making the decision, and
the ``market efficiency" condition, however, assumes a rational expected price
and implies that the pricing rule can be influenced by insider's strategy.

We study the price impact of order book events - limit orders, market orders
and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that,
over short time intervals, price changes are mainly driven by the order flow
imbalance, defined as the imbalance between supply and demand at the best bid
and ask prices. Our study reveals a linear relation between order flow
imbalance and price changes, with a slope inversely proportional to the market
depth. These results are shown to be robust to seasonality effects, and stable
across time scales and across stocks.

Statistical properties of double-auction markets with Bid-Ask spread in
market order are investigated through the response function. We first attempt
to utilize the so-called Madhavan-Richardson-Roomans model (MRR for short) to
simulate the stochastic process of the price-change in empirical data sets
(say, EUR/JPY or USD/JPY exchange rates) in which the Bid-Ask spread fluctuates
in time. We find that the MRR theory apparently fails to simulate so much as
the qualitative behaviour (`non-monotonic' behaviour) of the response function
calculated from the data.

By studying all the trades and best bids/asks of ultra high frequency
snapshots recorded from the order books of a basket of 10 futures assets, we
bring qualitative empirical evidence that the impact of a single trade depends
on the intertrade time lags. We find that when the trading rate becomes faster,
the return variance per trade or the impact, as measured by the price variation
in the direction of the trade, strongly increases. We provide evidence that
these properties persist at coarser time scales. We also show that the spread
value is an increasing function of the activity.

In this paper we introduce a simple model for a financial market
characterized by a single stock or good and an interplay between two different
traders populations, chartists and fundamentalists, which determine the price
dynamic of the stock. The model has been inspired by the microscopic
Lux-Marchesi model (T.Lux, M.Marchesi, Nature 397, (1999), 498--500). The
introduction of kinetic equations permits to study the asymptotic behavior of
the investments and the price distributions and to characterize the regimes of
lognormal behavior and the formation of power law tails.

We consider a heterogeneous agent-based economic model where economic agents
have strictly bounded rationality and where income allocation strategies evolve
through selective imitation. Income is calculated by a Cobb-Douglas type
production function, and selection of strategies for imitation depends on the
income growth rate they generate. We show that under these conditions, when an
agent adopts a new strategy, the effect on its income growth rate is
immediately visible to other agents, which allows a group of imitating agents
to quickly adapt their strategies when needed.

We study how information perturbations can destabilize two-sided matching
markets. In our model, agents arrive on the market over two periods, while
agents in the first period do not know the types of those arriving later.
Agents already present in the market may match early or wait for the small
group of new entrants. Despite the lack of discounting or risk aversion, this
perturbation creates incentives to match early and leave the market before the
new agents arrive.

In a financial market, for agents with long investment horizons or at times
of severe market stress, it is often changes in the asset price that act as the
trigger for transactions or shifts in investment position. This suggests the
use of price thresholds to simulate agent behavior over much longer timescales
than are currently used in models of order-books.

We show that many phenomena, routinely ignored in efficient market theory,
can be systematically introduced into an otherwise efficient market, resulting
in models that robustly replicate the most important stylized facts.

Traditional market makers are losing their importance as automated systems
have largely assumed the role of liquidity provision in markets. We update the
model of Glosten and Milgrom (1985) to analyze this new world: we add multiple
securities and introduce an automated market maker who uses the relationships
between securities to price order flow. This new automated participant
transacts the majority of orders, sets prices that are more efficient, and
increases informed and decreases uninformed traders' transaction costs.

Using high-frequency time series of stock prices and share volumes sizes from
January 2002-May 2009, this paper investigates whether the effects of the onset
of high-frequency trading, most prominent since 2005, are apparent in the
dynamics of the dollar traded volume. Indeed it is found in almost all of 14
heavily traded stocks, that there has been an increase in the Hurst exponent of
dollar traded volume from Gaussian noise in the earlier years to more
self-similar dynamics in later years.

Kinetic exchange models have been successful in explaining the shape of the
income/wealth distribution in the economies. However, such models usually make
some ad-hoc assumptions when it comes to determining the savings factor. Here,
we examine a few models in and out of the domain of standard neo-classical
economics to explain the savings behavior of the agents. A number of new
results are derived and the rest conform with those obtained earlier.
Connections are established between the reinforcement choice and strategic
choice models with the usual kinetic exchange models.

The gauge theory of arbitrage was introduced by Ilinski in
[arXiv:hep-th/9710148] and applied to fast money flows in
[arXiv:cond-mat/9902044]. The theory of fast money flow dynamics attempts to
model the evolution of currency exchange rates and stock prices on short, e.g.\
intra-day, time scales. It has been used to explain some of the heuristic
trading rules, known as technical analysis, that are used by professional
traders in the equity and foreign exchange markets.

Motivated by the literature on investment flows and optimal trading, we
examine intraday predictability in the cross-section of stock returns. We find
a striking pattern of return continuation at half-hour intervals that are exact
multiples of a trading day, and this effect lasts for at least 40 trading days.
Volume, order imbalance, volatility, and bid-ask spreads exhibit similar
patterns, but do not explain the return patterns. We also show that short-term
return reversal is driven by temporary liquidity imbalances lasting less than
an hour and bid-ask bounce.

We show that the statistics of spreads in real order books is characterized
by an intrinsic asymmetry due to discreteness effects for even or odd values of
the spread. An analysis of data from the NYSE order book points out that
traders' strategies contribute to this asymmetry.

We study a simple model of an asset market with informed and non-informed
agents. In the absence of non-informed agents, the market becomes information
efficient when the number of traders with different private information is
large enough. Upon introducing non-informed agents, we find that the latter
contribute significantly to the trading activity if and only if the market is
(nearly) information efficient.

We use techniques from network science to study correlations in the foreign
exchange (FX) market over the period 1991--2008. We consider an FX market
network in which each node represents an exchange rate and each weighted edge
represents a time-dependent correlation between the rates. To provide insights
into the clustering of the exchange rate time series, we investigate dynamic
communities in the network.

The goal of this article is to understand some interesting features of
sequences of arbitrage operations, which look relevant to various processes in
Economics and Finances. In the second part of the paper, analysis of sequences
of arbitrages is reformulated in the linear algebra terms. This admits an
elegant geometric interpretation of the problems under consideration linked to
the asynchronous systems theory. We feel that this interpretation will be
useful in understanding more complicated, and more realistic, mathematical
models in economics.

It has been suggested that marked point processes might be good candidates
for the modeling of financial high-frequency data. A special class of point
processes, Hawkes processes, has been the subject of various investigations in
the financial community. In this paper, we propose to enhance a basic order
book simulator with limit and market orders arrival times following mutually
(unsymmetrically) exciting Hawkes processes. Modeling is based on empirical
observations on interval times between orders that we verify on several markets
(equity, bond futures, index futures).

In this paper we examine inefficiencies and information disparity in the
Japanese stock market. By carefully analysing information publicly available on
the internet, an `outsider' to conventional statistical arbitrage
strategies--which are based on market microstructure, company releases, or
analyst reports--can nevertheless pursue a profitable trading strategy. A large
volume of blog data is used to demonstrate the existence of an inefficiency in
the market. An information-based model that replicates the trading strategy is
developed to estimate the degree of information disparity.

We observe the performances of three strategy evaluation schemes, which are
the history-dependent wealth game, the trend-opposing minority game, and the
trend-following majority game in a stock market where the price is exogenously
determined. The price is either directly adopted from the real stock market
indices or generated with the Markov chain of order $\le 2$. Each scheme's
success is quantified by average wealth accumulated by the traders equipped
with the scheme.

A representative investor generates realistic and complex security price
paths by following this trading strategy: if, a few ticks ago, the market asset
had two consecutive upticks or two consecutive downticks, then sell, and
otherwise buy. This simple, unique, and robust model is the smallest possible
deterministic model of financial complexity, and its generalization leads to
complex variety. Compared to a random walk, the minimal model generates time
series with fatter tails and more frequent crashes, thus more closely matching
the real world.

We consider optimal execution strategies for block market orders placed in a
limit order book (LOB). We build on the resilience model proposed by Obizhaeva
and Wang (2005) but allow for a general shape of the LOB defined via a given
density function. Thus, we can allow for empirically observed LOB shapes and
obtain a nonlinear price impact of market orders.

In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple order
book based model for the impact of large orders on stock prices. They use this
model to derive optimal strategies for the execution of large orders. We apply
these strategies to an agent-based stochastic order book model that was
recently proposed by Bovier, \v{C}ern\'{y} and Hryniv, but already the
calibration fails. In particular, from our simulations the recovery speed of
the market after a large order is clearly dependent on the order size, whereas
the AFS model assumes a constant speed.

We develop a theoretical trading conditioning model subject to price
volatility and return in terms of market psychological behavior, based on a
volume-price probability wave distribution in which we use transaction volume
probability to describe price volatility uncertainty and intensity.

A dynamic herding model with interactions of trading volumes is introduced.
At time $t$, an agent trades with a probability, which depends on the ratio of
the total trading volume at time $t-1$ to its own trading volume at its last
trade. The price return is determined by the volume imbalance and number of
trades. The model successfully reproduces the power-law distributions of the
trading volume, number of trades and price return, and their relations.
Moreover, the generated time series are long-range correlated.

We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the
development of financial instruments, with a dynamical picture of an
interacting market, in a simple setting. The proliferation of financial
instruments apparently provides more means for risk diversification, making the
market more efficient and complete.