## ABSTRACT

Second, this chapter develops a number of results concerning optimal international equity portfolio diversifi cation. It is well known that one of the most important decisions most agents (individuals, households and, at times, the treasury departments of fi rms) face is the choice of a portfolio of assets. is means that agents decide how much to invest (in the case of households, save) and in which assets. In particular, a huge body of literature exists that shows that equity portfolio diversifi cation should be pursed by aggressively diversifying an agent’s portfolio among stocks issued in many (better, all) countries. In this chapter, we write and solve by dynamic programming methods a typical asset allocation problem in which an expected power (constant relative risk aversion) utility maximizer proceeds to select portfolio shares under the two alternative statistical frameworks-pure-and jump-diff usions-entertained in our

analysis. e risk of event-related jumps in security prices and volatility, changes the standard dynamic portfolio choice problem in several important ways. In the classical pure-jump problem, security prices are continuous, and instantaneous returns have infi nitesimal standard deviations; as a result, an investor considers only small local changes in security prices when selecting the optimal portfolio. In the presence of jumps, the investor must also consider the eff ects of potentially large changes in security prices when selecting a dynamic portfolio strategy. Since the portfolio that is optimal for large returns need not be the same as the portfolio that is optimal for small returns, this creates a possible trade-off between considering continuous, “small” local changes that always occur in any (as small as one may consider) interval of time, and “large” price changes that do not always occur and in fact are unlikely to occur as the interval of time considered shrinks.