On the pricing of American options

The problem of valuation for contingent claims that can be exercised at any time before or at maturity, such as American options, is discussed in the manner of Bensoussan [1]. We offer an approach which both simplifies and extends the results of existing theory on this topic.

[1]  H. P. Jr. Mackean,et al.  Appendix : A free boundary problem for the heat equation arising from a problem in mathematical economics , 1965 .

[2]  P. Meyer.  Probability and potentials , 1966 .

[3]  A. G. Fakeev.  Optimal Stopping Rules for Stochastic Processes with Continuous Parameter , 1970 .

[4]  A. G. Fakeev.  Optimal Stopping of a Markov Process , 1971 .

[5]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[6]  P. Samuelson.  Mathematics of Speculative Price , 1973 .

[7]  Clifford W. Smith,et al.  Option pricing: A review , 1976 .

[8]  P. Moerbeke.  On optimal stopping and free boundary problems , 1973, Advances in Applied Probability.

[9]  J. Bismut,et al.  Temps d'arrÊt optimal, théorie générale des processus et processus de Markov , 1977 .

[10]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

[11]  池田 信行,et al.  Stochastic differential equations and diffusion processes , 1981 .

[12]  N. Karoui.  Les Aspects Probabilistes Du Controle Stochastique , 1981 .

[13]  L. Rogers.  Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[14]  H. Heyer.  Statistics of random processes I: General theory , 1983 .

[15]  J. Harrison,et al.  A stochastic calculus model of continuous trading: Complete markets , 1983 .

[16]  A. Bensoussan.  On the theory of option pricing , 1984, Acta Applicandae Mathematicae.