TY - JOUR
T1 - ℒp-Projections of random variables and its application to finance
AU - Arai, Takuji
N1 - Funding Information:
The author would like to thank an anonymous referee for helpful comments, which has greatly improved the paper. This research was supported by Grant-in-Aid for Young Scientists (B) No. 16740062 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
PY - 2008/12
Y1 - 2008/12
N2 - The aim of this paper is to give an extension of the mean-variance hedging problem to the $ ℒp-setting, where 1 < p < ∞. Remark that the mean-variance hedging is corresponding to the case where p = 2. Firstly, we prove that the unique existence of the optimal hedging strategy in the ℒp-sense, which is the ℒp-projection of the underlying contingent claim onto a suitable space of stochastic integrations. Next, we obtain its feedback representation under some additional assumptions. Moreover, the valuation problem induced by the ℒp-projections naturally is discussed.
AB - The aim of this paper is to give an extension of the mean-variance hedging problem to the $ ℒp-setting, where 1 < p < ∞. Remark that the mean-variance hedging is corresponding to the case where p = 2. Firstly, we prove that the unique existence of the optimal hedging strategy in the ℒp-sense, which is the ℒp-projection of the underlying contingent claim onto a suitable space of stochastic integrations. Next, we obtain its feedback representation under some additional assumptions. Moreover, the valuation problem induced by the ℒp-projections naturally is discussed.
KW - Mathematical finance
KW - Option pricing
KW - Q-optimal martingale measure
KW - Semimartingales
KW - Stochastic integrals
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U2 - 10.1142/S0219024908005068
DO - 10.1142/S0219024908005068
M3 - Article
AN - SCOPUS:59449110339
SN - 0219-0249
VL - 11
SP - 869
EP - 888
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 8
ER -