Andrea Mantovi

3-d lattice Yang-Mills free energy to four loops

We compute the expansion of the 3-d Lattice Yang-Mills free energy to four-loop order by means of Numerical Stochastic Perturbation Theory. The first and second order are already known and are correctly reproduced. The third- and fourth-order coefficients are new results. The known logarithmic divergence in the fourth order is correctly identified. We comment on the relevance of our computation in the context of dimensionally reduced finite temperature QCD.

Four loop stochastic perturbation theory in 3d SU(3)

Abstract Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g 8 , which had already been computed in the continuum.

A Theory of Hostile Takeovers

In this paper, a consistent picture of the multifaceted mechanism of a hostile leveraged takeover is provided. The analysis points out two basic issues. The first is the financial problem caused by the leveraged acquisition, which calls for detailed strategic planning in order to ascertain the feasibility of the operation with respect to the capital structure of the target company. The second issue is the agency problem caused by the delegation of the acquisition to a raider, who possesses the unique skills needed for such a task. A coherent framework has thus been developed, which enables the raider to evaluate different potential targets and the lender to guarantee the optimal behaviour of the agent.

Two and three loops computations of renormalization constants for lattice QCD

Renormalization constants can be computed by means of Numerical Stochastic Perturbation Theory to two/three loops in lattice perturbation theory, both in the quenched approximation and in the full (unquenched) theory. As a case of study we report on the computation of renormalization constants of the propagator for Wilson fermions. We present our unquenched ( N f = 2) computations and compare the results with non perturbative determinations.

On Risk Aversion and Prudence

Building on the isomorphism between the theories of risk aversion and precautionary saving, an objective index of prudent behavior is introduced, which generalizes the riskiness index set forth by Aumann and Serrano (2008). A benchmark framework for the monotone relation between risk aversion and prudence results, in which absence of level effects and stochastic dominance of shocks are crucial, and generalized risk measures enable us to embed the fundamental result set forth by Menegatti (2007). Effective maps of completely proper rationality (Mantovi, 2013) enable one to parametrize departure from our benchmark framework in terms of level effects which preserve the positive effect of absolute risk aversion on absolute prudence.

Dividends, Sustainability and Relevance

Sustainability and economic relevance of dividend policies are addressed in terms of an optimal control model set forth by Feichtinger et al. (2007), by means of which two different capitalization measures, accounting for dividends and capital gains, can be given explicit representation. In the light of the theory of capital tailored by Dorfman (1969), an intertemporal economic measure of shareholder value is introduced, together with the associated shadow price. Relevant tradeoffs and scale effects are thoroughly discussed, in connection with the Modigliani-Miller irrelevance framework. The ratio between the value function and the hamiltonian function is conjectured to represent a sound parallel to the price-earnings ratio. The lens property of the model provides a setting for discussing conditions for the rationality of myopic policymaking.

Venture Capital, R&D and Incentives: Analytic Approach

RD on the other hand, the agency problem, raised by the delegation of the research commitment, is solved along the lines of the Principal-Agent model, with the characterization of the optimal tradeoffs between incentives and profits, and therefore of the optimal contract between the principal and the research team. Such an approach has a general significance in a corporate governance perspective, in particular in high-tech industries such as the pharmaceutical one.

3-d lattice SU(3) free energy to four loops

We report on the perturbative computation of the 3d lattice Yang-Mills free energy to four loops by means of Numerical Stochastic Perturbation Theory. The known first and second orders have been correctly reproduced; the third and fourth order coefficients are new results and the known logarithmic IR divergence in the fourth order has been correctly identified. Progress is being made in switching to the gluon mass IR regularization and the related inclusion of the Faddeev-Popov determinant.

Preliminary results in unquenched numerical stochastic perturbation theory

Abstract Introducing fermionic loops contributions in Numerical Stochastic Perturbation Theory was mainly motivated by the proposal to compute 2–3 loops for renormalization constants (and improvement coefficients). This is feasible because the computational overhead of unquenching NSPT is by far lower than for non perturbative simulations. We report on first, preliminary results for the quark propagator (basically the third loop for the critical mass) and discuss the status of the computation of other quantities.