Economics Insights @ CBS

Likelihood ratios are used in computer simulation to estimate expectations with respect to one law from simultation of another. This importance sampling technique can be implemented with either the likelihood ratio at the end of the simulated time horizon or with a sequence of likelihood ratios at intermediate times. Since a likelihood ratio process is a martingale, the intermediate values are conditional expectations of the final value and their use introduces no bias.

Firms registered outside the United States and listed on a primary U.S. exchange may provide their U.S. shareholders with financial statements prepared under their domestic (non-U.S.) generally accepted accounting principles (GAAP). The Securities and Exchange Commission requires such firms to reconcile their reported earnings and shareholders' equity to U.S. GAAP as part of a Form 20-F filing. These reconciliations provide a set of precise measures of the differences created by alternative accounting practices.

If the score in a squash game is tied late in the game, one player has a choice of how many additional points (from a prespecified set of possibilities) are to be played to determine the winner. This paper constructs a Markov chain model of the situation and solves for the optimal strategy. Expressions for the optimal strategy are obtained with a symbolic algebra computer package. Results are given for both international and American scoring systems. The model and analysis are very suitable for educational purposes.