Below is a paragraph from an academic paper. Polish the writing to meet the academic style, improve the spelling, grammar, clarity, concision and overall readability. When necessary, rewrite the whole sentence. Note in particular that the polished version of the paragraph should first be written in full, then list all modification and explain the reasons to do so in markdown table.
In this paper, we investigate the pricing issue of options on the maximum or the minimum of multi-assets, taking into account the possibility of counterparty default before the options reach maturity. To determine the price, we give the joint distribution of the minimum value of one Brownian motion and the terminal values of all Brownian motions for correlated multidimensional Brownian motion. The joint distributions we obtain for the Brownian motion can also be applied to other pricing problems involving multi-asset options subject to default risk prior to maturity. By employing measure change techniques, we derive a closed-form formula for valuing these options. We also provide numerical examples to demonstrate our findings.
