Salvatore Federico
Growth and agglomeration in the heterogeneous space: a generalized AK approach
We provide an optimal growth spatio-temporal setting with capital accumulation and diffusion across space to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. The problem is set as a optimal control problem of a PDE and treated by dynamic programming methods in infinite dimension. In sharp contrast to the related literature, which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology and population. Both the transitional spatio-temporal dynamics and the asymptotic spatial distributions are computed in closed form. Concerning the latter, we find, among other results, that: (i) due to inequality aversion, the consumption per capital distribution is much flatter than the distribution of capital per capita; (ii) endogenous spillovers inherent in capital spatio-temporal dynamics occur as capital distribution is much less concentrated than the (pre-specified) technological distribution; (iii) the distance to the center (or to the core) is an essential determinant of the shapes of the asymptotic distributions, that is relative location matters.
Andrea Pallavicini
Smile Modelling in Commodity Markets
We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to deal with the limited number of options quoted in the market. Cleared commodity markets for futures and options are analyzed to include in the pricing framework specific trading clauses and margining procedures. Numerical examples for calibration and pricing are provided for different commodity products.
Athena Picarelli
Optimal control under controlled loss constraints via reachability approach and compactification
We study optimal control problems under controlled loss constraints at several fixed dates. It is well known that for such problems the characterization of the value function by a Hamilton-Jacobi-Bellman equation requires additional strong assumptions involving an interplay between the set of constraints and the dynamics of the controlled system. To treat the problem in absence of these assumptions we first translate it into a state-constrained stochastic target problem and then apply a level-set approach to describe the reachable set. The main advantage of our approach is that it allows us to easily handle the state constraints by an exact penalization. However, this target problem involves a new set of control variables that are unbounded. A ``compactification'' of the problem is then performed.
Frank Riedel
Viability and arbitrage under Knightian uncertainty
We reconsider the microeconomic foundations of financial economics under Knightian Uncertainty. We do not assume that agents (implicitly) agree on a common probabilistic description of the world. We rather base our analysis on a common ordering of contracts, a much weaker requirement. The economic viability of asset prices and the absence of arbitrage are equivalent; both are closely related to the existence of nonlinear pricing measures. We show how the different versions of the Efficient Market Hypothesis are related to the assumptions we are willing to impose on the market's ordering of contracts. Our approach also unifies recent versions of the Fundamental Theorem of Asset Pricing under a common framework.