Anderson Economic Group Work

Practical Dynamic Programming for Business and Forensic Economics (AEG Working Paper, 2005-05)

One of the most important applications of forensic economics is estimating lost profits in commercial disputes and lost earnings of workers in cases of injury. The most common method for estimating such damages has been to reconstruct them using an “income” or “discounted cash flow” approach, based on assumptions about how similar workers or firms operate. Such methods can work well if the static assumptions accurately capture the dynamic optimization that actual workers and managers perform.

Another approach is to use the optimization technique of “dynamic programming,” introduced by mathematician Richard Bellman in 1957. Such a method can be utilized to estimate losses of income for workers or businesses, and do so while explicitly modeling the optimization behavior of the persons involved. This method has emerged as the tool of choice for many difficult optimization questions in finance and economics in the academic world, and it was recently introduced as a method applicable to business valuation.

In this paper, we (1) motivate the use of this method, using the concept of intertemporal optimization by a consumer; (2) describe the fundamental technique of dynamic programming, which converts an potentially intractable problem involving multiple variables and many time periods into a 2-period problem that may be tractable; (3) outline simple models for lost earnings of workers and lost profits for business; and (4) briefly note the history of the technique and cite sources for the mathematical and computational issues not addressed in this paper. An appendix includes an example business valuation problem that has been solved using this technique and recently-developed computational software.

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