Abstract
This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework. Under the assumption that the option can be continuously traded without friction just as the stock, a dynamic relationship between their optimal positions is derived by using the stochastic dynamic programming techniques. The dynamic option pricing equations are also established. In particular, the properties of the associated solutions are discussed and their explicit representations are demonstrated via the Feynman-Kac formula. This paper further compares the dynamic option price to the existing price notions, such as the marginal price and indifference price.
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This research is supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814901, the National Natural Science Foundation of China under Grant Nos. 11101215 and 61304065, and the Program of Natural Science Research of Jiangsu Higher Education Institutions of China under Grant No. 12KJB110011.
This paper was recommended for publication by Editor DI Zengru.
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Mi, H., Zhang, S. Dynamic valuation of options on non-traded assets and trading strategies. J Syst Sci Complex 26, 991–1001 (2013). https://doi.org/10.1007/s11424-013-1198-2
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DOI: https://doi.org/10.1007/s11424-013-1198-2