The price of sudden disclosure of inside information on stock market

We consider a discrete model of insider trading in terms of repeated games with incomplete information. The solution of the bidding game of beforehand unlimited duration was obtained by V. Domansky (2007). Insider's optimal strategy $\sigma^m$ in the infinite stage game generates the simple random walk of posterior probabilities over the lattice $l/m$, $l=0,\ldots,m$, with absorption at the extreme points 0 and 1 and provides the expected gain $1/2$ per step to an insider. In this paper we calculate the insider's profit in the game of any finite duration when he applies the strategy $\sigma^m$. It is shown that this strategy is his $\varepsilon$-optimal strategy in $n$-stage game, where $\varepsilon$ decreases exponentially as $n\to\infty$. This means that the sequence of $n$-stage game values converges to the value of infinite game at least exponentially. The result obtained is interpreted as the loss of the insider in the case of sudden disclosure of his private information. For the special case we compare obtained insider's profit with the exact game value (result of V. Kreps, 2009) and demonstrate that the error term in the case of optimal insider's behaviour also decreases exponentially. Bibliogr. 6.