Agent Network Topology

Topological theory of intelligent agent networks provides crucial information about the structure of agent distribution over a network. Agent network topologies not only take agent distribution into consideration, but also consider agent mobility and intelligence in a network. Current research in the agent network topology area adopts topological theory from the distributed system andcomputing network fields, such as LAN without considering mobility and intelligence aspects. Moreover, current agent network topology theory is not systematic and relies on graph-based methodology, which is inefficient in describing large-scale agent networks.

Related Work

The term, agent network topology, is derived from mathematical topological theory. This concept overlaps with topological theory in data communications and distributed systems areas.

Existing topological theories in the computing field have been mainly applied to data communications and distributed systems areas. These theories have made some extraordinary contributions. However, as an emerging discipline, topological theory in multi-agent systems is inadequate. Existing topological theory cannot fulfill the needs of an agent network because an agent network has its specific characteristics, which include mobility, intelligence, and flexibility. Agent network topologies take not only agent distribution into consideration but also consider agent mobility in a network. Most of the current research work in the agent network topology area adopts topological theory from the distributed system and computing network fields without considering mobility and intelligence aspects.

Current research work in the agent network topology area is also not systematic and relies on graph-based methodology. Graph-based topological analysis of a network topology is often based on the network graph provided and sometimes lacks precise measurements of each agent. Moreover, existing agent network topologies are incapable of providing detailed information about each agent and its relationship with other agents on a network. This increases the difficulty of agent communication and cooperation, such as agent searching or matching, over a network. Thus, the research direction of agent network topologies needs to follow these three characteristics based on some concrete network performance analysis.

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Mathematical finance

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Mathematical finance is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive and extend the mathematical or numerical models suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock (see: Valuation of options).
In terms of practice, mathematical finance also overlaps heavily with the field of computational finance (also known as financial engineering). Arguably, these are largely synonymous, although the latter focuses on application, while the former focuses on modeling and derivation (see: Quantitative analyst). The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance. Many universities around the world now offer degree and research programs in mathematical finance; see Master of Mathematical Finance.
Contents [hide]
1 History: Q versus P
1.1 Derivatives pricing: the Q world
1.2 Risk and portfolio management: the P world
2 Criticism
3 Mathematical finance articles
3.1 Mathematical tools
3.2 Derivatives pricing
4 See also
5 Notes
6 References
7 External links
[edit]History: Q versus P

There exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other hand. One of the main differences is that they use different probabilities, namely the risk-neutral probability, denoted by "Q", and the actual probability, denoted by "P".
[edit]Derivatives pricing: the Q world
The goal of derivatives pricing is to determine the fair price of a given security in terms of more liquid securities whose price is determined by the law of supply and demand. Examples of securities being priced are plain vanilla and exotic options, convertible bonds, etc. Once a fair price has been determined, the sell-side trader can make a market on the security. Therefore, derivatives pricing is a complex "extrapolation" exercise to define the current market value of a security, which is then used by the sell-side community.
Derivatives pricing: the Q world
Goal "extrapolate the present"
Environment risk-neutral probability
Processes continuous-time martingales
Dimension low
Tools Ito calculus, PDE’s
Challenges calibration
Business sell-side
Quantitative derivatives pricing was initiated by Louis Bachelier in The Theory of Speculation (published 1900), with the introduction of the most basic and most influential of processes, the Brownian motion, and its applications to the pricing of options. However, Bachelier's work hardly caught any attention outside academia.
Main article: Black–Scholes
The theory remained dormant until Fischer Black and Myron Scholes, along with fundamental contributions by Robert C. Merton, applied the second most influential process, the geometric Brownian motion, to option pricing. For this M. Scholes and R. Merton were awarded the 1997 Nobel Memorial Prize in Economic Sciences. Black was ineligible for the prize because of his death in 1995.
The next important step was the fundamental theorem of asset pricing by Harrison and Pliska (1981), according to which the suitably normalized current price P0 of a security is arbitrage-free, and thus truly fair, only if there exists a stochastic process Pt with constant expected value which describes its future evolution:





(1 )
A process satisfying (1) is called a "martingale". A martingale does not reward risk. Thus the probability of the normalized security price process is called "risk-neutral" and is typically denoted by the blackboard font letter "".
The relationship (1) must hold for all times t: therefore the processes used for derivatives pricing are naturally set in continuous time.
The quants who operate in the Q world of derivatives pricing are specialists with deep knowledge of the specific products they model.
Securities are priced individually, and thus the problems in the Q world are low-dimensional in nature. Calibration is one of the main challenges of the Q world: once a continuous-time parametric process has been calibrated to a set of traded securities through a relationship such as (1), a similar relationship is used to define the price of new derivatives.
The main quantitative tools necessary to handle continuous-time Q-processes are Ito’s stochastic calculus and partial differential equations (PDE’s).
[edit]Risk and portfolio management: the P world
Risk and portfolio management aims at modelling the probability distribution of the market prices of all the securities at a given future investment horizon.
This "real" probability distribution of the market prices is typically denoted by the blackboard font letter "", as opposed to the "risk-neutral" probability "" used in derivatives pricing.
Based on the P distribution, the buy-side community takes decisions on which securities to purchase in order to improve the prospective profit-and-loss profile of their positions considered as a portfolio.

Fibonacci Who?

We will be using Fibonacci ratios a lot in our trading so you better learn it and love it like your mother's home cooking. Fibonacci is a huge subject and there are many different Fibonacci studies with weird-sounding names but we're going to stick to two: retracement and extension.

Let us first start by introducing you to the Fib man himself...Leonardo Fibonacci.



No, Leonardo Fibonacci isn't some famous chef. Actually, he was a famous Italian mathematician, also known as a super duper uber ultra geek.

He had an "Aha!" moment when he discovered a simple series of numbers that created ratios describing the natural proportions of things in the universe.

The ratios arise from the following number series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

This series of numbers is derived by starting with 1 followed by 2 and then adding 1 + 2 to get 3, the third number. Then, adding 2 + 3 to get 5, the fourth number, and so on.

After the first few numbers in the sequence, if you measure the ratio of any number to the succeeding higher number, you get .618. For example, 34 divided by 55 equals .618.

If you measure the ratio between alternate numbers you get .382. For example, 34 divided by 89 = 0.382 and that's as far as into the explanation as we'll go.

These ratios are called the "golden mean". Okay that's enough mumbo jumbo. With all those numbers, you could put an elephant to sleep. We'll just cut to the chase; these are the ratios you HAVE to know:

Fibonacci Retracement Levels
0.236, 0.382, 0.500, 0.618, 0.764

Fibonacci Extension Levels
0, 0.382, 0.618, 1.000, 1.382, 1.618

You won't really need to know how to calculate all of this. Your charting software will do all the work for you. Besides, we've got a nice Fibonacci calculator that can magically calculate those levels for you. However, it's always good to be familiar with the basic theory behind the indicator so you'll have the knowledge to impress your date.

Traders use the Fibonacci retracement levels as potential support and resistance areas. Since so many traders watch these same levels and place buy and sell orders on them to enter trades or place stops, the support and resistance levels tend to become a self-fulfilling prophecy.




Traders use the Fibonacci extension levels as profit taking levels. Again, since so many traders are watching these levels to place buy and sell orders to take profits, this tool tends to work more often than not due to self-fulfilling expectations.

Most charting software includes both Fibonacci retracement levels and extension level tools. In order to apply Fibonacci levels to your charts, you'll need to identify Swing High and Swing Low points.

A Swing High is a candlestick with at least two lower highs on both the left and right of itself.

A Swing Low is a candlestick with at least two higher lows on both the left and right of itself.

You got all that? Don't worry, we'll explain retracements, extensions, and most importantly, how to grab some pips using the Fib tool in the following sections.