Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach

Autor:	Jussi Lindgren
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	information theory financial markets entropy stochastic optimal control options pricing Black–Scholes equation Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 22, Iss 11, p 1283 (2020)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e22111283
Popis:	This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/791098893cb84ff3a0f5519c20304074 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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