A discrete-time model of American put option in an uncertain environment
A discrete-time model of American put option in an uncertain environment
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DOI：
10.1016/s0377-2217(02)00591-x
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发表时间：
2003-11
期刊：
影响因子：
--
通讯作者：
Y. Yoshida
中科院分区：
文献类型：
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作者：
Y. Yoshida
建立了不确定美式看跌期权的离散时间数学模型，从模糊期望的角度考虑决策者的主观判断，用概率期望和可能性测度定义的模糊期望来评价随机性和模糊性.给出了模糊随机过程中最优停止问题的最优性方程，并给出了美式看跌期权的最优执行时间。证明了在合理的假设下，最优模糊价格是最优性方程的解。给出了美式看跌期权中卖方最优期望价格的允许范围，并通过算例讨论了最优期望价格的意义和性质。在一个数值例子中，讨论了连续时间模型的离散时间近似模型。
A discrete-time mathematical model for American put option with uncertainty is presented, and the randomness and fuzziness are evaluated by both probabilistic expectation and fuzzy expectation defined by a possibility measure from the viewpoint of fuzzy expectation, taking account of decision-maker’s subjective judgment. An optimality equation for the optimal stopping problem in a fuzzy stochastic process is derived and an optimal exercise time is given for the American put option. It is shown that the optimal fuzzy price is a solution of the optimality equation under a reasonable assumption. The permissible range of the writer’s (seller’s) optimal expected price in the American put option is presented, and the meaning and properties of the optimal expected prices are discussed in numerical examples. In a numerical example, the discrete-time approximation model is discussed for the continuous-time model.