| This paper mainly studies the optimal schedules and pricing American options.American option pricing is a more difcult problem, the most fundamental reasonis that the option to get the most optimal expected discounted profts when imple-menting that we don’t know in advance, and must treat it as part of the solution.Using the language of mathematics is to solve a partial diferential equation withdynamic boundary, namely with free boundary, Black-Scholes equation, which iscalled dynamic boundary problem, and this kind of problem only in very specialcircumstances have analytical solution. On the other hand, the American optionpricing problem in essence is the optimal stopping problem.Therefore, if some op-timal stopping problem can be reasonable and efective to solve, American optionpricing problem is solved. So this article use1997M.Beibel and2001H.R.Lerchetwo articles in the literature of the brown exponential martingale method to solvethe problem of optimal stopping, we discuss the permanent American put optionsin dual currency model, get the optimal schedules τ and options of the initial valueof V0expression. Optimal stopping theory is a strong application background inprobability theory. In real life, we will face all kinds of decisions. With the theory ofoptimal stopping solve the problem of perpetual American options, only is a goodexample to solve the problem of fnancial decision making. On the other hand, dueto the expanding international fnancial market, every investor may use the localcurrency to investment risk assets of foreign currency, to seek the risk assets (notonly for the American Option) of the best selling time, be equal to optimal stoppingproblem in the model of. Therefore, in this paper, in the dual currency model, usingthe above specifc martingale method to discuss the optimal stopping problem, getthe implicit expression of the optimal stopping time, which is of great signifcanceto the fnancial decision-making. |
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