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BUYING AND SELLING RULES FOR A SIMPLE TRANSACTION OF A MEAN-REVERTING ASSET

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We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.

Abstract

We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.

참고문헌 (10)

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  2. Guo, X., "Closed-form solutions for perpetual american put options with regime switching", SIAM J. Appl. Math, 64, pp.2034~2049 (2004)
  3. Fama, E., "Forecasting Pro¯tability and Earnings", J. of Business, 73(2), pp.161~175 (2000)
  4. Frankel, J., "A panel project on purchasing power parity: Mean reversion within and between countries", J. of International Economics, 40, pp.209~224 (1996)
  5. McKean, H.P., "A free boundary problem for the heat equation arising from a problem of mathematical economics", Inderstrial Managem. Review, 61, pp.32~39 (1965)
  6. Shin, D., "American perpetual put option valuation with one time regime switching" (2009)
  7. Song, Q.S., "Stochastic Optimization Methods for Buying-Low- and-selling-High Strategies", Stochastic Analysis and Applications, 27(3), pp.523~542 (2009)
  8. Uhlenbeck, G.E., "On the theory of Brownian Motion", Physical Review, 36, pp.823~841 (1930)
  9. Mean Reversion in Stock Prices: Evidence and Implication, "Poterba, J.", NBER, ~, pp.NBER Working paper 2343 (1987)
  10. Zhang, H., "Trading a mean-reverting asset: Buy law and sell high", Auto- matica, 44, pp.1511~1518 (2008)

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