Основы российского рынка криптовалют: монография
Analyzing the reasons of financial crises in the book «The Black Swan» N.N. Taleb concludes that modern economic models badly describe reality for they are not able to forecast such crises in advance. We tried to present processes on stock exchange as two random processes one of which happens rather often (regular regime) and the other one - rather rare. Our answer is that if regular processes are correctly recognized with the probability a bit higher than 1/2, this allows to get positive average gain. We believe that this very phenomenon lies in the basis of unwillingness of people to expect crises permanently and to try recognizing them.
ФИНАНСОВЫЕ КРИЗИСЫ, биржа, пуассоновский процесс, financial crises, Stock exchange, Poisson processes
We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer value.
The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G1(p). We offer the solutions for these games.
We begin with constructing solutions for these games with distributions p having two and three-point supports. Next, we build the optimal strategies of Player 1 for bidding games G1(p) with arbitrary distributions p as convex combinations of his optimal strategies for such games with distributions having two- and three-point supports. To do this we construct the symmetric representation of probability distributions with fixed integer expectation vectors as a convex combination of distributions with not more than three-point supports and with the same expectation vectors.