Abstract
We study the optimal growth rate in the market where there are a saving asset and a low liquid risky asset. In this paper the low liquid asset can be traded at random trade times. We show the optimal growth rate both with finite time horizon and with infinite time horizon. And we find an optimal strategy. Further we discuss the convergence of the optimal growth rate and the optimal strategy as the time horizon goes to infinity.
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References
Boyle, P., Vorst, T.: Option replication in discrete time with transaction costs. J. Finance47, 271–293 (1992)
Cetin, U., Jarrow, R., Protter, P.: Liquidity risk and arbitrage theory. Finance and Stochastics8, 311–341 (2004)
Cvitanic, J., Karatzas, I.: On portfolio optimization under drawdown control. IMA Volumes in Mathematics and Its Applications65, 35–46 (1995)
Davis, M.H.A., Norman A.R.: Portfolio selection with transaction costs. Math. Oper. Res.15, 676–713 (1990)
Grossman, S.J., Zhou, Z.: Optimal investment strategies for controlling draw downs. Math. Finance3, 241–276 (1993)
Kabanov, Yu.: Hedging and liquidation under transaction costs in currency mar kets. Finance and Stochastics3, 237–248 (1999)
Kusuoka, S.: Limit theorem on option replication cost with transaction costs. Ann. Appl. Probab.5, 198–221 (1995)
Leland, H.E.: Option pricing and replication with transactions costs. J. Finance40, 1283–1301 (1985)
Matsumoto, K.: Optimal portfolio of low liquid assets with a power utility func tion. J. Math. Sci. The University of Tokyo 10, 687–726 (2003)
Matsumoto, K.: Optimal portfolio of low liquid assets with a log—utility function. Finance and Stochastics10, 121–145 (2006)
Merton, R.C.: Optimum consumption and portfolio rules in a continuous time model. J. Econ. Theory3, 373–413 (1971)
Rogers, L.C.G.: The relaxed investor and parameter uncertainty. Finance and Stochastics5, 131–154 (2001)
Rogers, L.C.G., Zane, O.: A simple model of liquidity effects. In: Sandmann, K. et al. (eds.): Advances in finance and stochastics: Essays in honour of Dieter Sondermann. Berlin: Springer 2002, pp. 161–176
Subramanian, A., Jarrow, R.: The liquidity discount. Math. Finance11, 447–474 (2001)
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Matsumoto, K. (2009). Optimal growth rate in random trade time. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advance in Mathematical Economics, vol 12. Springer, Tokyo. https://doi.org/10.1007/978-4-431-92935-2_5
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DOI: https://doi.org/10.1007/978-4-431-92935-2_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-92934-5
Online ISBN: 978-4-431-92935-2
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