Using the language of convex analysis we describe key results in several important areas of finance: portfolio theory, financial derivative trading and pricing and consumption based asset pricing theory. We hope to emphasize the importance of convex analysis in financial mathematics and also bring attention to researchers in convex analysis interesting issues in financial applications.

Domestic investors hold a substantially larger proportion of their wealth portfolios in domestic assets than standard portfolio theory would suggest, a phenomenon called "equity home bias." In the absence of this bias, investors would optimally diversify domestic output risk using foreign equities. Therefore, consumption growth rates would tend to comove across countries even when output growth...

In this article we have reviewed ``Modern Portfolio Analysis'' and outlined some important topics for further research. Issues discussed include the history and future of portfolio theory, the key inputs necessary to perform portfolio optimization, speci®c problems in applying portfolio theory to ®nancial institutions, and the methods for evaluating how well portfolios are managed. Emphasis is ...

International asset demands are functions of expected returns. Optimal portfolio theory tells us that the coetlicients in this relationship depend on the variance-covariance matrix of real returns. But previous estimates of the optimal portfolio (1) assume expected returns constant and (2) are not set up to test the hypothesis of mean-variance optimization. We use maximum likelihood estimation ...