Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach

We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies only a kind of symmetry condition on its behavior at infinity, but no restriction on its growth rate is imposed. Thanks to strong integrability properties of invariant measures $\mu$, solvability of the associated Kolmogorov equation in $L^1(\mu)$ is then established, and the infinitesimal generator of the transition semigroup is identified as the closure of the Kolmogorov operator. A key role is played by a generalized variational setting.Comment: 32 page

Fr\'echet differentiability of mild solutions to SPDEs with respect to the initial datum

We establish n-th order Fr\'echet differentiability with respect to the initial datum of mild solutions to a class of jump-diffusions in Hilbert spaces. In particular, the coefficients are Lipschitz continuous, but their derivatives of order higher than one can grow polynomially, and the (multiplicative) noise sources are a cylindrical Wiener process and a quasi-left-continuous integer-valued random measure. As preliminary steps, we prove well-posedness in the mild sense for this class of equations, as well as first-order G\^ateaux differentiability of their solutions with respect to the initial datum, extending previous results in several ways. The differentiability results obtained here are a fundamental step to construct classical solutions to non-local Kolmogorov equations with sufficiently regular coefficients by probabilistic means.Comment: 30 pages, no figure

A variational approach to dissipative SPDEs with singular drift

We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which no continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in spaces of continuous, or bounded, functions in space and time. Our approach combines variational techniques with a priori estimates, both pathwise and in expectation, on solutions to regularized equations.Comment: 35 page

The Regulation of Interdependent Markets

We examine the issue of whether two monopolists which produce substitutable goods should be regulated by one (centralization) or two (decentralization) regulatory authorities, when the regulator(s) can be partially captured by industry. Under full information, two decentral- ized agencies - each regulating a single market - charge lower prices than a unique regulator, making consumers better off. However, this leads to excessive costs for the taxpayers who subsidize the …rms, so that centralized regulation is preferable. Under asymmetric informa- tion about the firms' costs, lobbying induces a unique regulator to be more concerned with the industry's interests, and this decreases social welfare. When the substitutability between the goods is high enough, the firms'lobbying activity may be so strong that decentralizing the regulatory structure may be social welfare enhancing.regulation, lobbying, asymmetric information, energy markets

Incentives to (irreversible) investments under different regulatory regimes

This paper addresses the issue of how regulatory constraints affect firm's investment choices when the firm has the option to delay investment. The "RPI-x" rule is compared to a profit sharing rule, which increases the x factor in case profits go beyond a given level. It is shown that these rules are identical in their impact on investment choices, in that the change in the option value exactly compensates the change in the ``direct'' profitability of investment. The result is then analysed in the light of option theory and explained on the basis of the ``bad news principle''.

Incentives to (Irreversible) Investments Under Different Regulatory Regimes

This paper addresses the issue of how regulatory constraints affect firm's investment choices when the firm has the option to delay investment. The RPI-x rule is compared to a profit sharing rule, which increases the x factor in case profits go beyond a given level. It is shown that these rules are identical in their impact on investment choices, in that the change in the option value exactly compensates the change in the “direct“ profitability of investment. The result is then analysed in the light of option theory and explained on the basis of the “bad news principle“.

Take or Pay Contracts and Market Segmentation

This paper examines competition in the liberalized natural gas market. Each .firm has zero marginal cost core capacity, due to long term contracts with take or pay obligations, and additional capacity at higher marginal costs. The market is decentralized and the firms decide which customers to serve, competing then in prices. In equilibrium each .firm approaches a different segment of the market and sets the monopoly price, i.e. market segmentation. Antitrust ceilings do not prevent such an outcome while the separation of wholesale and retail activities and the creation of a wholesale market induces generalized competition and low margins in the retail segment.Entry, Segmentation, Decentralized market