Dear Colleagues,

Stochastic difference equations and systems of stochastic difference equations usually refer to unpredictable events. The solution of stochastic difference equations is a stochastic process. Stochastic difference equations can be thought of as discrete time approximations of stochastic differential equations.

Stochastic models are interesting in their own right and as such,  their study is one  of the purposes of this section. Furthermore, this section focuses its study within specific   applications, of such types of equations, related with the stock market and in particular, with algorithmic trading or high-frequency trading.

A group of six people four of them employees of the Futures Trading Commission and two market representatives established “a definition” of high-frequency trading published on June 22, 2012, in a Special Issue of Futures Industry Association.

Among others, some of the basic characteristics of such algorithms are: decision making, order initiation, routing or execution without human transaction, low-latency technology designed such that response times are minimum, high message rates (orders, quotes cancellations).  Computerised trading is estimated to account for half the shares traded in the United States, although other types of traders try to curb certain services for high-frequency traders. Defenders of high-frequency trading say that the practice makes trading easier and cheaper for investors of all kinds.

Stochastic equations studied in this section might as well consider the metrics of price impact, liquidity, volatility, and volume in electronic markets whose participants along with high-frequency traders also contain among others: financial companies, market makers, fundamental and technical traders.

The equations might focus to closed form solutions in the case of analytic approach, or even dynamic programming techniques solving Optimization problems related to market portfolios. It should be clear to the authors of this section that their study of stochastic model might as well be independent from  applications to high frequency, algorithmic or other type of trading. Additionally, welcome are the trading models whose empirical evidence and numerical or statistical analysis evaluation contains high levels of stochastic patterns. Finally, in some special cases papers examining difference equations might as well be considered for publication in this session.

Dr. Elias Camouzis
Prof. Dr. John Leventides
Guest Editors

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