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cs, and chaotic systems in general, is discussed in section 6 below. As discussed above, Lotka-Volterra models have been used in Marxian analysis by Goodwin and others, though the models can be somewhat complex. The models presented above seem more efficacious than the Goodwin type Lotka-Volterra model
andom walk process has been removed from it's many body background, and individual prices are treated as moving randomly isolated by themselves. But Black-Scholes is simply the diffusion equation, and things don't diffuse with random jumps in a vacuum. The random movements of dust particles undergoing Brownia
that this chaotic motion is noticeable in objects as large as planets. This is not simply the chaos of quantum effects or the stochasticity found in Black-Scholes. This is 'deterministic chaos' or usually 'chaos theory'. The chaos is present even in problems that can be described in exact mathematics and are
naturally from the companies model. During the modelling process I was rereading Steve Keen's 'Debunking Economics' and had also read some of the Goodwin modelling work while investigating the ratio of returns to labour and capital. It seemed to me that by combining the wealth, company and commodity m
The research on liquidity suggests two implications for finance that are both quite profound, the first area relates to the pricing models based on Black-Scholes, the second to the pricing of shares under the CAPM. Almost all modern option pricing theory is based on the Black-Scholes model, or other closely-
sible), then it may be that measurement of liquidity might be able to give good timely measures for current volatility that can be used directly in Black-Scholes models; rather than the current practice of imputing from historical volatility. A second significant area of interest for the application of liqui
s 3.4 Commodity models Background Modelling Results Discussion - Background - Modelling - Results - Discussion 4. Minsky goes Austrian a la Goodwin — Macroeconomic Models 4.1 Macroeconomic Models - Background 4.2 Macroeconomic Models - Modelling 4.3 Macroeconomic Models - Results 4.4 Macroeco
ists working in finance have not only accepted this, but they have built more and more baroque models on these flimsy foundations. The trouble with Black-Scholes is that it works very well, except when it doesn't. This basic flaw has been pointed out from Mandlebrot onwards, to date with no notice taken. Thi
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