Conditional Distribution of the Limit Order Book Given the History of the Best Quote Process

Recently, models of limit order markets, particularly those of the continuous double auction, are subject to an intense research. Due to their complexity, the models are regarded to be analytically intractable. In the present paper, nonetheless, a closed form result is derived: the conditional distribution of the limit order book given the history of the best quote process.limit order markets, continuous double auction, limit order book, conditional distribution, immigration-death process

Stochastic Model of Thin Market with Divisible Commodity

We suggest a model of (a thin) market at which the number of participants is random with Poisson distribution. We provide a formula for joint distribution of the market price and the traded volume. We derive an asymptotic distribution of the quantities. We find that, according to our model, with increasing intensity of the participants' number, the fluctuations of the market price vanish while the variance of the traded volume increases.thin market, market price, traded volume, asymptotic distribution

Forecasting in Continuous Double Auction

Recently, the continuous double auction, i.e. the trading mechanism used in the majority of the financial markets, is the subject of an extensive study. In the present paper, a model of the continuous double auction with the completely random flow of the limit orders is studied. The main result of the paper is an approximate formula for the distribution of the market price and the traded volume at the time s given the information available at tlimit order markets, continuous double auction, price and volume, forecasting, market microstructure

Stochastic Model of Thin Market of nondivisible commodity

We assume a thin market with finite number of buyers and sellers, each agent having a single jump demand xor supply function (the jump is unit). Further, we assume that number of each agent's arrival is a Poisson distributed random variable. We describe the joint distribution of the market price and of the traded volume. Further, we examine a model with infinite number of agents (which may serve as an approximation of the model with the finite number of agents). Again, we describe the joint distribution of the price and the volume.Thin market, market price, traded volume

Normal Approximation of the Disrtibution of the Equilibrium Price in Markets with Random Demand and Supply

In the paper, the asymptotic distribution of the equilibrium price in markets with the random demand and supply is described. Two special cases - the one with smooth demand and supply curves and the one with jump demand and supply curves - are studied. It is found that in both the cases the fluctuations of the price vanish at the rate O(n^{-1/2}) as the number of the agents n tends to infinity. Finally, a normal approximation of the distribution of the equilibrium price is suggested.equilibrium price, random demand, random supply, asymptotic distribution, normal approximation

Reputation, corporate social responsibility and market regulation

The paper investigates the role of the government and self-regulatory reputation mechanisms to internalise externalities of market operation. If it pays off for companies to invest in a good reputation by an active policy of corporate social responsibility (CSR), external effects of the market will be (partly) internalised by the market itself. The strength of the reputation mechanism depends on the functioning of non governmental organisations (NGOs), the transparency of the company, the time horizon of the company, and on the behaviour of employees, consumers and investors. On the basis of an extensive study of the empirical literature on these topics, we conclude that in general the working of the reputation mechanism is rather weak. Especially the transparency of companies is a bottleneck. If the government would force companies to be more transparent, it could initiate a self-enforcing spiral that would improve the working of the reputation mechanism. We also argue that the working of the reputation mechanism will be weaker for smaller companies and for both highly competitive and monopolistic markets. We therefore conclude that government regulation is still necessary, especially for small companies.Corporate social responsibility; market regulation

A technique for adding range restrictions to generalized searching problems

In a generalized searching problem, a set $S$ of $n$ colored geometric objects has to be stored in a data structure, such that for any given query object $q$, the distinct colors of the objects of $S$ intersected by $q$ can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp.\ fat triangles) with a fat triangle (resp.\ point). For both problems, a data structure is obtained having size $O(n^{1+\epsilon})$ and query time $O((\log n)^2 + C)$. Here, $C$ denotes the number of colors reported by the query, and $\epsilon$ is an arbitrarily small positive constant

Compatible 4-Holes in Point Sets

Counting interior-disjoint empty convex polygons in a point set is a typical Erd\H{o}s-Szekeres-type problem. We study this problem for 4-gons. Let $P$ be a set of $n$ points in the plane and in general position. A subset $Q$ of $P$, with four points, is called a $4$-hole in $P$ if $Q$ is in convex position and its convex hull does not contain any point of $P$ in its interior. Two 4-holes in $P$ are compatible if their interiors are disjoint. We show that $P$ contains at least $\lfloor 5n/11\rfloor {-} 1$ pairwise compatible 4-holes. This improves the lower bound of $2\lfloor(n-2)/5\rfloor$ which is implied by a result of Sakai and Urrutia (2007).Comment: 17 page