On power series expansions of the S-resolvent operator and the Taylor formula

The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of $S$-spectrum and of $S$-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus, the proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the $S$-resolvent operators associated to the sum of two $n$-tuples of operators. This result is a crucial step in the proof of our main results,but it is also of independent interest because it gives a new series expansion for the $S$-resolvent operators. This paper is devoted to researchers working in operators theory and hypercomplex analysis

Financial Globalization and Real Regionalization

Over the period 1972-1986, the correlations of GDP, employment and investment between the United States and an aggregate of Europe, Canada and Japan were respectively 0.76, 0.66, and 0.63. For the period 1986 to 2000 the same correlations were much lower: 0.26, 0.03 and -0.07 (real regionalization). At the same time, U.S. international asset trade has significantly increased. For example, between 1972 and 1999, United States gross FDI and equity assets in the same group of countries rose from 4 to 23 percent of the U.S. capital stock (financial globalization). We document that the correlation of real shocks between the U.S. and the rest of the world has declined. We then present a model in which international financial market integration occurs endogenously in response to less correlated shocks. Financial integration further reduces the international correlations in GDP and factor supplies. We find that both less correlated shocks and endogenous financial market development are needed to account for all the changes in the international business cycle.

The international diversification puzzle is not as bad as you think

In simple one-good international macro models, the presence of non-diversifiable labor income risk means that country portfolios should be heavily biased toward foreign assets. The fact that the opposite pattern of diversification is observed empirically constitutes the international diversification puzzle. We embed a portfolio choice decision in a frictionless two-country, two-good version of the stochastic growth model. In this environment, which is a workhorse for international business cycle research, we derive a closed-form expression for equilibrium country portfolios. These are biased towards domestic assets, as in the data. Home bias arises because endogenous international relative price fluctuations make domestic stocks a good hedge against non-diversifiable labor income risk. We then use our theory to link openness to trade to the level of diversification, and find that it offers a quantitatively compelling account for the patterns of international diversification observed across developed economies in recent years.Investments, Foreign ; International trade - Econometric models

The International Diversification Puzzle Is Not as Bad as You Think

In simple one-good international macro models, the presence of non-diversifiable labor income risk means that country portfolios should be heavily biased toward foreign assets. The fact that the opposite pattern of diversification is observed empirically constitutes the international diversification puzzle. We embed a portfolio choice decision in a frictionless two-country, twogood version of the stochastic growth model. In this environment, which is a workhorse for international business cycle research, we derive a closed-form expression for equilibrium country portfolios. These are biased towards domestic assets, as in the data. Home bias arises because endogenous international relative price fluctuations make domestic stocks a good hedge against non-diversifiable labor income risk. We then use our our theory to link openness to trade to the level of diversification, and find that it offers a quantitatively compelling account for the patterns of international diversification observed across developed economies in recent years.Home bias, international diversification

Financial Globalization and Real Regionalization

Over the period 1972-1986, the correlations of GDP, employment and investment between the United States and an aggregate of Europe, Canada and Japan were respectively 0.76, 0.66, and 0.63. For the period 1986 to 2000 the same correlations were much lower: 0.26, 0.03, and -0.07 (real regionalization). At the same time, U.S. international asset trade has significantly increased. For example, between 1972 and 1999, United States gross FDI and equity assets in the same group of countries rose from 4 to 23 percent of the U.S. capital stock (financial globalization). We argue that these two trends are intimately related. We document that the correlation of real shocks between the U.S. and the rest of the world has declined. We then present a model in which international financial market integration occurs endogenously in response to less correlated shocks. Financial integration further reduces the international correlations in GDP and factor supplies. We find that both less correlated shocks and endogenous financial market development are needed to account for all the changes in the international business cycle