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National Repository of Grey Literature 2 records found  Search took 0.03 seconds. 
Conditional distributions and condeitional expectations
 Čellár, Matúš ; Hlubinka, Daniel (advisor) ; Janák, Josef (referee)
This paper discusses conditional distributions and conditional expectations, their introduction and basic properties. We begin with the definition of conditional probability, show a few theorems and demonstrate their application on an example. From there we move on to the conditioning with respect to random events and discrete random variables. In the general case we help ourselves with the definition of conditional expectation as random variable, show its properties, ways of expression and the fact that the introduction in the discrete case does not lead to a contradiction with the general definition. Then we deduce the criteria that have to be met for the conditional distribution to exist and in the last part we solve a number of theoretical problems.
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Zjednodušení modelu Smitha a Farmera
 Šmíd, Martin
We formulate a model of a limit order market, very similar to this of Smith at al. [2003]. We describe analytically the conditional distribution of the state of the market (i.e. the shapes of the limit order books) given the history of the bid and ask quotes. Thanks to this result, we may construct estimates of (usually unknown) shape of the order book based on a history of the quotes (which is usually available). Further, we are able to test statistically the validity of the model. In addition, our results allow us to specify the (conditional) distribution of the inter-event times and the jumps of the quotes which may help us to speed up eventual simulations of the system significantly.
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