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Quantile hedging for an insider

100%

Klusik P. , Palmowski Z. , Zwierz J.

Probability and Mathematical Statistics

2010

tom Vol. 30, Fasc. 2

247--258

In this paper we consider the problem of the quantile hedging from the point of view of a better informed agent acting on the market. The additional knowledge of the agent is modelled by a filtration initially enlarged by some random variable. By using equivalent martingale measures introduced in [1] and [2] we solve the problem for the complete case, by extending the results obtained in [4] to the insider context. Finally, we consider the examples with the explicit calculations within the standard Black–Scholes model.

On existence of local martingale measures for insiders who can stop at honest times

88%

Zwierz J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom Vol. 55, no 2

183-192

We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time A. We show, using the multiplicative decomposition of the Azema supermartingale, that if the martingale part of the price process has the predictable representation property and A satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider. This extends the results obtained by Imkeller to the continuous semimartingale setting and general honest times.