- Title
- Financial applications of non-extensive thermodynamics: some philosophical considerations
- Creator
- Juniper, James
- Relation
- Fifth Australian Society of Heterodox Economists Conference. Essays in Heterodox Economics: Fifth Australian Society of Heterodox Economists Conference (Sydney 11-12 December, 2006) p. 249-264
- Relation
- http://www.asb.unsw.edu.au/research/societyofheterodoxeconomists/Pages/default.aspx
- Publisher
- Society of Heterodox Economists
- Resource Type
- conference paper
- Date
- 2006
- Description
- This focus of this paper is on financial applications of non-extensive thermodynamics. It begins by examining three common ways of generalizing the stochastic calculus to accommodate Tsallis distributions. The first of these is based on developing generalised information measures that extend principles of statistical inference to account for nonextensivity. This approach has the advantage of identifying the relationship between nonextensivity and uncertainty aversion. The second approach generalizes the logarithmic functions, which appear in the differential equation satisfied by the constrained entropic functional. In the third approach, based on an interpretation of generalized diffusion equations, emphasis is placed on the link between fractional and q-generalized diffusion processes and alternative forms of calculus including fractional derivatives and Jackson's derivative. Next, the paper provides an overview of research accounting for the ubiquity of nonextensivity in stochastic processes. Included here, are recent q-generalizations of the standard central limit theorem and its Lévy-Gnedenko counterpart; the emergence of power law distributions in scenarios characterised by finite dimension or fluctuation effects; and research into the properties of the z-logistic equation. For this non-linear recursive difference equation, trajectories at the 'edge of chaos' are characterised q-generalized Liapunov functions and sensitivity measures. Finally, the paper returns to consider the issue of uncertainty aversion by reviewing the debate occasioned by Zanette and Montemurro's paper, which criticizes non-thermodynamical applications of nonextensive statistics. While Constantino Tsallis has responded effectively to these and other criticisms, it is argued that the Zanette and Montemurro critique does serve to highlight an obvious gap in justifications made for financial applications of non-extensive statistics. In is argued that an alternative justificatory strategy would place renewed emphasis on the implications of the nonextensivity property for decision-making under uncertainty.
- Subject
- thermodynamics; Tsallis distributions; stochastic calculus; financial applications
- Identifier
- uon:9181
- Identifier
- http://hdl.handle.net/1959.13/920583
- Identifier
- ISBN:9780733424175
- Language
- eng
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