Quantile hedging for an insider

• Autorzy: Klusik P. , Palmowski Z. , Zwierz J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

insider trading; quantile hedging; initial enlargement of filtrations; equivalent martingale measure

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 2
• Strony: 247--258
• Opis fizyczny: Bibliogr. 10 poz., tab.

Twórcy

autor

Klusik P.

• University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Palmowski Z.

• University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Zwierz J.

• University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] J. Amendinger, Martingale representation theorems for initially enlarged filtrations, Stochastic Process. Appl. 89 (1) (2000), pp. 101-116.
• [2] J. Amendinger, P. Imkeller and M. Schweizer, Additional logarithmic utility of an insider, Stochastic Process. Appl. 75 (2) (1998), pp. 263-286.
• [3] D. Duffie and C. F. Huang, Multiperiod security markets with differential information, J. Math. Econom. 15 (1986), pp. 283-303.
• [4] H. Föllmer and P. Leukert, Quantile hedging, Finance Stoch. 3 (3) (1999), pp. 251-273.
• [5] H. Föllmer and P. Leukert, Efficient hedging: cost versus shortfall risk, Finance Stoch. 4 (2) (2000), pp. 117-146.
• [6] A. Grorud and M. Pontier, Probabilités neutres au risque et asymétrie d’information, C. R. Acad. Sci. Paris Sér. I Math. 329 (11) (1999), pp. 1009-1014.
• [7] T. Jeulin, Semi-martingales et grossissement d’une filtration, Lecture Notes in Math. No 833, Springer, Berlin 1980.
• [8] T. Jeulin and M. Yor (Eds.), Grossissements de filtrations: exemples et applications, Lecture Notes in Math. No 1118, Springer, Berlin 1985. Papers from the seminar on stochastic calculus held at the Université de Paris VI, Paris 1982/83.
• [9] I. Karatzas and I. Pikovsky, Anticipative portfolio optimization, Adv. in Appl. Probab. 28 (1996), pp. 1095-1122.
• [10] J. Zwierz, On existence of local martingale measures for insiders who can stop at honest times, Bull. Polish Acad. Sci. Math. 55 (2) (2007), pp. 183-192.