We use a PDE argument to deal with the mathematical analysis of the valuation of American options on the maximum/minimum of two assets. There are several factors which affect the valuation of options, such as stock price, strike price, the time to expiry, volatilities, the correlation constant, the risk-free interest rate and dividends. The first problem we are concerned with here is what happens to the prices of options if one of these factors is increasing while the others remain fixed. In the second part of this paper, the properties of the optimal exercise boundary of option as free boundary of the parabolic obstacle problem are studied such as monotonicity, convexity and asymptotic behavior.
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Lishang Jiang, Analysis of pricing American options on the maximum (minimum) of two risk assets. Interfaces Free Bound. 4 (2002), no. 1, pp. 27–46DOI 10.4171/IFB/51