A note on a moving boundary problem arising in the American put option. (English) Zbl 1152.91522

Knessl, Charles

Stud. Appl. Math. 107, No. 2, 157-183 (2001).

Summary: “We consider an American put option, under the Black-Scholes model. This corresponds to a moving boundary problem for a PDE. We convert the problem to a nonlinear integral equation for the moving boundary, which corresponds to the optimal exercise of the option. We use singular perturbation methods to compute the moving boundary, as well as the full solution to the PDE, in various asymptotic limits. We consider times close to the expiration date, as well as systems where the interest rate is large or small, relative to the volatility of the asset for which the option is sold.”
Additional references are: I. Karatzas, Lectures on the mathematics of finance, CRM Monograph Series. 8. Am. Math. Soc., Providence, RI (1996; Zbl 0878.90010) and S. D. Jacka, Math. Finance 1, No. 2, 1–14 (1991; Zbl 0900.90109).

MSC:

91B28	Finance etc. (MSC2000)
60H30	Applications of stochastic analysis (to PDEs, etc.)