A new method to solve fuzzy stochastic finance problem

Abstract

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.

Citation

Dash, J.K., Panda, S. and Panda, G.B. (2022), "A new method to solve fuzzy stochastic finance problem", Journal of Economic Studies, Vol. 49 No. 2, pp. 243-258. https://doi.org/10.1108/JES-10-2020-0521