• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.543-552
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• 2012

Parrondo paradox is a counter-intuitive phenomenon where two losing games can be combined to win or two winning games can be combined to lose. When we trade stocks with a history-dependent Parrondo game rule (where we buy and sell stocks based on recent investment outcomes) we found Parrondo paradox in stock trading. Using stock data of the KRX from 2008 to 2010, we analyzed the Parrondo paradoxical cases in the Korean stock market.

• Journal of the Korean Data and Information Science Society
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• v.23 no.5
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• pp.867-880
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• 2012

Parrondo paradox is the counter-intuitive situation where individually losing games can combine to win or individually winning games can combine to lose. In this paper, we derive the expected profit per trade for each portfolio when we trade stocks everyday under the spatially dependent Parrondo game rule. Using stock data of KRX (Korea Exchange) from 2008 to 2010, we show that Parrondo paradox exists in the stock trading.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.77-87
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• 2015

Parrondo paradox is the counter-intuitive phenomenon where two losing games can be combined to win or two winning games can be combined to lose. In this paper, we consider an ensemble of players, one of whom is chosen randomly to play game A' or game B. In game A', the randomly chosen player transfers one unit of his capital to another randomly selected player. In game B, the player plays the history-dependent Parrondo game in which the winning probability of the present trial depends on the results of the last two trials in the past. We show that Parrondo paradox exists in this redistribution model of the history-dependent Parrondo game.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.781-790
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• 2015

The Parrondo paradox is the counter-intuitive phenomenon: when we combine two losing games we can win the game or when we combine two winning games we can lose the game. In this paper, we assume that an investor adopts the rule of the history-dependent Parrondo game for investment in the stock market. Using the KRX (Korea Exchange) data from 2012 to 2014, we found the Parrondo paradox in the stock trading: the redistribution of profits among accounts can turn the decrease of the expected cumulative profit into the increase of the expected cumulative profit. We also found that the opposite case, namely the reverse Parrondo effect, can happen in the stock trading.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1241-1251
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• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.745-753
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• 2014

Parrondo paradox is the counter-intuitive situation where individually losing games can combine to win or individually winning games can combine to lose. In this paper, we compare the history-dependent Parrondo games and the space-dependent Parrondo games played cooperatively by the multiple players. We show that there is a probability region where the history-dependent Parrondo game is a losing game whereas the space-dependent Parrondo game is a winning game.

• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.631-641
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• 2011

We consider a history-dependent Parrondo game in which the winning probability of the present trial depends on the results of the last two trials in the past. When a fraction of an infinite number of players are allowed to choose between two fair Parrondo games at each turn, we compare the blind strategy such as a random sequence of choices with the short-range optimization strategy. In this paper, we show that the random sequence of choices yields a steady increase of average profit. However, if we choose the game that gives the higher expected profit at each turn, surprisingly we are not supposed to get a long-run positive profit for some parameter values.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.311-321
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• 2008

Mathematical paradoxes may arise when computations give unexpected results. We use three paradoxes to illustrate how they work in the basic probability theory. In the process of resolving the paradoxes, we expect that student-teachers can pedagogically gain valuable experience in regards to sharpening their mathematical knowledge and critical reasoning.