Bookkeeping

We obtain the Monte-Carlo value of this derivative by generating N lots of M normal variables, creating N sample paths and so N values of H, and then taking the average.Commonly the derivative will depend on two or more (possibly correlated) underlyings. Today’s value of the derivative is found by taking the expectation over all possible samples and discounting at the risk-free rate. For simpler situations, however, simulation is not the better solution because it is very time-consuming and computationally intensive. Many problems in mathematical finance entail the computation of a particular integral (for instance the problem of finding the arbitrage-free value of a particular derivative). Essentially, the…

At the end of a given reporting period, any net income that is not paid out to shareholders is added to the business’s retained earnings. Therefore, the more often a company pays dividends to its shareholders, the more its retained earnings balance gets reduced. The difference between the beginning balance and the ending balance indicates the change in retained earnings during the accounting period. Hence retained earnings are the company’s past earnings that have been kept by the company instead of being distributed to shareholders as dividends. For example, a company might be able to reclassify the deficit (e.g., decrease additional paid-in capital and increase retained earnings up…