Stochastic differential equations with imprecisely defined parameters in market analysis

Risk and uncertainties plays a major role in stock market investments. It is a pedagogical practice to deduce probability distributions for analysing stock market returns using theoretical models of investor behaviour. Generally, economists estimate probability distributions for stock market returns that are observed from the history of past returns. Besides this, there are impreciseness involved in various factors affecting market investment and returns. As such, we need to model a more reliable strategy that will quantify the uncertainty with better confidence. Here, we have presented a computational method to solve fuzzy stochastic Volterra–Fredholm integral equation which is based on the block pulse functions (BPFs) using fuzzy stochastic operational matrix (SOM). The concept of fuzziness has been hybridized with BPFs, and the corresponding stochastic integral equation has been modelled. For illustration, the developed model has been used to investigate an example problem of Black–Scholes fuzzy stochastic differential equation (FSDE), and the results are compared in special cases.