Self-duality and associated parallel or cocalibrated G2{\mathrm{G}}_2 structures

We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated. The study starts with a recast of the Singer-Thorpe equations of 4-dimensional geometry. These are applied to the Bryant-Salamon cons\-truction of complete $\mathrm{G}_2$-holonomy metrics on the vector bundle of self- or anti-self-dual 2-forms on $M$. We then discover new examples of that special holonomy on disk bundles over ${\cal H}^4$ and ${\cal H}^2_{\mathbb{C}}$, respectively, the real and complex hyperbolic space. Only in the end we present the new $\mathrm{G}_2$ structures on principal bundles.Comment: 20 pages; final version, to appear in Annales Academi{\ae} Scientiarum Fennic{\ae

Variations of gwistor space

We study natural variations of the G2 structure {\sigma}_0 \in {\Lambda}^3_+ existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M. We find a circle of structures for which the induced metric is the usual one, the so-called Sasaki metric, and prove how the original structure has a preferred role in the theory. We deduce the equations of calibration and cocalibration, as well as those of W3 pure type and nearly-parallel type.Comment: 16 page

Weighted metrics on tangent sphere bundles

Natural metric structures on the tangent bundle and tangent sphere bundles $S_rM$ of a Riemannian manifold $M$ with radius function $r$ enclose many important unsolved problems. Admitting metric connections on $M$ with torsion, we deduce the equations of induced metric connections on those bundles. Then the equations of reducibility of $TM$ to the almost Hermitian category. Our purpose is the study of the natural contact structure on $S_rM$ and the $G_2$-twistor space of any oriented Riemannian 4-manifold.Comment: Accepted and about to appear in Quarterly Journal of Mathematics. 16 pages. This was the final draft submitted, before print proof

A fundamental differential system of Riemannian geometry

We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree $n$ associated to any given oriented Riemannian manifold $M$ of dimension $n+1$. The framework is that of the tangent sphere bundle of $M$. We generalise to a Riemannian setting some results from the theory of hypersurfaces in flat Euclidean space. We give new applications and examples of the associated Euler-Lagrange differential systems.Comment: Final version, very close to the one published; 32 p

The Forward Premium Puzzle in a Model of Imperfect Information: Theory and Evidence

This paper studies the forward premium puzzle in an environment where private agents do not perfectly observe the shocks that drive monetary policy. Private agents optimally update their conditional expectations by means of the Kalman filter. The transition dynamics associated with Kalman filtering lead to fixed time-effects and conditional heteroskedasticity in the forward premium regression. I provide evidence for the presence of time-effects in the forward premium regression and find that the forward premium puzzle is significantly weakened. In particular, a 1 percent increase in the 1-month interest differential is expected to be accompanied by an additional 0.34 percent depreciation of the currency in the following month.Forward premium puzzle, imperfect information, Kalman filter, fixed time-effects

The Composition of International Capital Flows: Risk Sharing Through Foreign Direct Investment

Evidence on international capital flows suggests that foreign direct investment (FDI) is less volatile than other financial flows. To explain this finding, I model international capital flows under the assumptions of imperfect enforcement of financial contracts and inalienability of FDI. Imperfect enforcement of contracts leads to endogenous financing constraints and the pricing of default risk. Inalienability implies that it is not as advantageous to expropriate FDI relative to other flows. These features combine to give a risk sharing advantage to FDI over other capital flows. This risk sharing advantage of FDI translates into a lower default premium and lower sensitivity to changes in a country's financing constraint. The model offers the new implication that financially constrained countries should borrow relatively more through FDI. This is because FDI is harder to expropriate and not because FDI is more productive or less volatile. Using several creditworthiness and country risk ratings to measure financing constraints, I present new evidence linking FDI and financing constraints. Moreover, numerical simulations of the model generate stronger serial correlation for FDI than for other flows into developing countries. This corroborates the view that non-FDI flows are more short-term and more likely to change direction.Foreign direct investment, intangible assets, volatility, risk sharing, imperfect enforcement, financing constraints, default risk, country risk

Optimal Currency Hedging

This paper characterizes optimal currency hedging in several models of downside risk. We consider, in turn, three models of hedging: (i) a firm that chooses its hedging policy in the presence of bankruptcy costs; (ii) an all equity firm that faces a convex tax schedule; and (iii) a firm whose manager is subject to loss aversion. In all these models, and contrary to conventional wisdom, we show that forwards dominate options as hedges of downside risk.Currency hedging, forwards, options, bankruptcy costs, taxes, loss aversion, downside risk

Optimal Lending Contracts and Firm Dynamics

We develop a general model of lending in the presence of endogenous borrowing constraints. Borrowing constraints arise because borrowers face limited liability and debt repayment cannot be perfectly enforced. In the model, the dynamics of debt are closely linked with the dynamics of borrowing constraints. In fact, borrowing constraints must satisfy a dynamic consistency requirement: The value of outstanding debt restricts current access to short term capital, but is itself determined by future access to credit. This dynamic consistency is not guaranteed in models of exogenous borrowing constraints, where the ability to raise short term capital is limited by some prespecified function of debt. We characterize the optimal default-free contract -which minimizes borrowing constraints at all histories- and derive implications for firm growth, survival, and leverage. The model is qualitatively consistent with stylized facts on the growth and survival of firms. Comparative statics with respect to technology and default constraints are derived.Financial constraints, imperfect enforcement, firm dynamics, capital structure, debt maturity.

Agency Conflicts, Investment, and Asset Pricing

The separation of ownership and control allows controlling shareholders to pursue private benefits. We develop an analytically tractable dynamic stochastic general equilibrium model to study asset pricing and welfare implications of imperfect investor protection. Consistent with empirical evidence, the model predicts that countries with weaker investor protection have more incentives to overinvest, lower Tobin's q, higher return volatility, larger risk premium, and higher interest rate. Calibrating the model to the Korean economy reveals that perfecting investor protection increases the stock market's value by 22 percent, a gain for which outside shareholders are willing to pay 11 percent of their capital stock.