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Similarities between Market Behavior and Network Traffic

Similarities between Market Behavior and Network Traffic. Shigeki Goto Waseda University. Black – Scholes. http://en.wikipedia.org/wiki/Black-Scholes. The Black–Scholes model is a mathematical model of the market for an equity, in which the equity's price is a stochastic process .

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Similarities between Market Behavior and Network Traffic

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  1. Similarities between Market Behavior and Network Traffic Shigeki Goto Waseda University

  2. Black–Scholes http://en.wikipedia.org/wiki/Black-Scholes • The Black–Scholes model is a mathematical model of the market for an equity, in which the equity's price is a stochastic process. • The Black–Scholes PDE is a partial differential equation which (in the model) must be satisfied by the price of a derivative on the equity. • The Black–Scholes formula is the result obtained by solving the Black-Scholes PDE for European put and call options.

  3. Black–Scholes • Merton and Scholes received the 1997 Nobel Prize in Economics for this and related work. Black was ineligible for the prize because of his death in 1995. dSt= μStdt+ σStdWt The price of the underlying instrumentSt follows a Wiener processWt with constant drift μ and volatility σ, and the price changes are log-normally distributed: ブラック-ショールズモデルとは、1 種類の配当のない株と 1 種類の債券の 2 つが存在する証券市場のモデルで、時刻 t における株価 St と債券価格 Bt が dSt= St(σdWt+ μdt), Bt= exp(rt) , r,σ,μは定数 , Wtは標準ブラウン運動,を満たすものをいう。 ja.wikipedia.org/wiki/ブラック-ショールズ方程式

  4. Network Traffic • Our diffusion equation is similar to that taken by Blackand Scholes who modeled the option pricing behavioras a geometric Brownian motion. • http://dspace.wul.waseda.ac.jp/dspace/bitstream/2065/4894/1/93038_391.pdf Yoshitaka Takahashi, A branching Poisson Process Input Finite-Capacity Queueing System for Telecommunication Networks, Waseda Commercial Review, vol.391, pp.105—116, Dec 2001.

  5. Fractal and Multifractal • Benoit B. Mandelbrot, A Multifractal Walk Down Wall Street, Scientific American, February 1999.http://www.elliottwave.com/education/SciAmerican/Mandelbrot_Article2.htm • Benoit B. Mandelbrot and Richard L. Hudson, The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin, and Reward, 2004. • (In Japanese, Econophysics)高安秀樹「経済物理学の発見」光文社新書１６７, 2004.

  6. Random Walk vs. Fractal A Multifractal Walk Down Wall Street Burton G. Malkiel,Random Walk Down Wall Street:The Time-Tested Strategy for Successful Investing

  7. Fractal Koch curve ja.wikipedia.org/wiki/コッホ曲線

  8. Network Traffic Tatsuya Mori, PhD Thesis, Waseda Universtiy, 2005 histogram CapturedPackets Pr [X (ti) = x] X (ti) asymmetric ti X (ti) histogram normal distribution (fGn model) X (ti) symmetric Pr [X (ti) = x] ti X (ti)

  9. Power Function (High volume AS numbers)

  10. Lessons • It is not possible to predict stock prices by the new theory. • The old model underestimates the risk because it uses random walk, or normal distribution. • Network traffic:95% rule of SLA is reasonable?

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