arXiv subjects
Publications and source records attributed to Yaroslav Ivanenko.
It is shown that absence of arbitrage opportunity in financial markets is a particular case of existence of uncertainty in decision system. Absence of arbitrage opportunity is considered in the sense of the Arrow-Debreu model of financial market with a riskless asset, while uncertainty (or ambiguity) is defined on the basis of the principle of internal coherence of M. Allais.
The article presents a translation of some widespread financial terminology into the language of decision theory. For instance, financial leverage can be regarded as an object of choice or a decision. We show how the optics of decision theory allows perceiving the recently introduced metrics of see-through-leverage, which proved to be very useful in understanding the phenomenology of the recent economic crisis. The importance for practical decision making of specification of the statistical regularity of the random phenomena at hand as well as of the rationality class of the decision maker is discussed.
A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular cases. We show that in the general case of nonstochastic randomness the minimal expected profit of uncovered European option position is always negative. A version of delta hedge is proposed.