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Generalized Moran process
Svoboda, Jakub ; Šámal, Robert (advisor) ; Balko, Martin (referee)
The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1
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Generalized Moran process
Svoboda, Jakub ; Šámal, Robert (advisor) ; Balko, Martin (referee)
The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1
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Market making jako obchodní strategie
Čamaj, Matej ; Stádník, Bohumil (advisor) ; Fičura, Milan (referee)
The purpose of this thesis is to analyze market making trading strategy and explore possibilities of using such strategy for intraday trading on the markets with the limit order book. In theoretical part we prove profitability of specified market making strategy under certain assumptions and moreover analyze effect of change of parameters on the performance of the strategy using one dimensional stochastic processes. Next the assumption of constant fair price is relaxed which leads to deterioration of profitability of these strategies. Because one dimensional stochastic processes do not capture price creation in the real world, we propose stochastic model of intraday trading in the next chapter. Advantage of this approach is that we can observe state of the limit order book during whole trading session and therefore better simulate conditions for test of the strategies. Although proposed model exhibit many phenomenons observed in empirical data like volatility clustering, in some situations it produces unrealistically high spread caused by the construction of the model, because arrivals of market and limit orders are modeled as independent processes. Another disadvantages are need of relatively extensive data for model calibration and high sensitivity of model to change of parameters. Lastly we test three different market making strategies under different choice of model parameters and show that expected profitability is positive in all cases.
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Simulace stochastických modelů hromadné obsluhy
Slámová, Kateřina ; Jablonský, Josef (advisor) ; Kuncová, Martina (referee)
Práce vystihuje teoretické poznatky z oblasti teorie hromadné obsluhy a simulace a následně jsou aplikovány poznatky do praxe. Pro případovou studii je využíván simulační software Simul8 a podpůrný program Crystal Ball, pomocí nichž je vytvořen model. Cílem je navrhnout nejlepší řešení daného problému a zhodnotit systém z hlediska struktury a funkčnosti. S modelem je provedeno několik experimentů a následně je posouzena vhodnost či nevhodnost použití jednotlivých variant.
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