On Sticky Bookmaking as a Learning Device in Horse-Racing Betting Markets

We present a stochastic dynamic model of the adjustment of betting odds by bookmakers in a horse-racing betting market. We use optimal stopping theory in a two-horse benchmark model with both informed and noise punters. A costly learning process discloses what information the informed traders possess and a risk-neutral bookmaker selects a stopping time at which the betting odds for each horse in a race are adjusted. Our main finding shows that an increased fraction of informed punters has a non-monotonic effect on the loss per trade to the bookmaker. We also find that as the fraction of noise traders goes up, the learning process is less informative, so that the decision to change the prices for each horse is taken sooner