By Peskir G.
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26) holds. The proof is complete. 1) can be extended to the case of a general (not necessarily continuous) semimartingale in the multidimensional setting of functions which are smooth above and below surfaces (instead of curves). Some of these extensions will be studied in a subsequent publication. REFERENCES 1. Eisenbaum, N. (2000). Integration with respect to local time. Potential Anal. 13, 303–328. 2. , and Shiryayev, A. N. (1995). Quadratic covariation and an extenˆ formula. Bernoulli 1, 149–169.
On the American option problem. Math. Finance. 15, 169–181. 6. , and Yor, M. (1999). Continuous Martingales and Brownian Motion. Springer, Berlin.
2002). The Implicit Function Theorem. Birkh¨auser, Boston. 4. Pedersen, J. , and Peskir, G. (2002). On nonlinear integral equations arising in problems of optimal stopping. Proc. Funct. Anal. VII (Dubrovnik 2001), Various Publ. Ser. No. 46, 159–175. 5. Peskir G. (2005). On the American option problem. Math. Finance. 15, 169–181. 6. , and Yor, M. (1999). Continuous Martingales and Brownian Motion. Springer, Berlin.
A Change-of-Variable Formula with Local Time on Curves by Peskir G.