Abstract
We consider a European option pricing problem under a partial information market, i.e., only the security’s price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering technique to solve a utility maximization problem under partial information through transforming the problem under partial information into the classical problem.
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The research was supported in part by National Natural Sciences Foundation of China under Grants 71101099 and 71571125, and the Fundamental Research Funds for the Central Universities under Grants 2014SCU04A06.
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Wu, M., Lu, J. & Huang, Nj. On European option pricing under partial information. Appl Math 61, 61–77 (2016). https://doi.org/10.1007/s10492-016-0122-1
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DOI: https://doi.org/10.1007/s10492-016-0122-1