Purpose

The authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.

Design/methodology/approach

The B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.

Findings

First, the authors are studying some various paper and some stochastic books.

Originality/value

This is a new technique.

中文翻译：

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一种求解模糊随机金融问题的新方法

目的

作者讨论了模糊环境下投资组合和 Black-Scholes (B-S)-期权定价模型的价值。

设计/方法/方法

B-S期权定价模型（OPM）是OPM在金融中的重要作用。在这里，每一个决定都是在不确定的情况下做出的。由于随机性或模糊性，这些不确定性可能是随机的或模糊的或两者兼而有之。由于漂移μ，波动程度s、利率r、执行价格k以及投资组合价值V ( t )、市场价格S _0 ( t ) 和看涨期权C ( t ) 的价值并不确切知道，因此它们被视为正模糊数。导出了模糊对数正态分布的偏期望。也是投资组合在任何时间t的价值并推导了模糊环境下的 B-S OPM。举例说明了 B-S OPM 的数值示例。

发现

首先，作者正在研究一些不同的论文和一些随机书籍。

原创性/价值

这是一种新技术。