Farm household risk balancing : implications for policy from an EU perspective

Purpose - Building on the risk balancing theory and on recent discussions the appropriateness of using farm income maximization as behavioural assumption, this paper extends the risk balancing framework by accounting for business-household interactions. The purpose of this paper is to theoretically introduce the concept of farm household risk balancing, a theoretical framework in which the farm household sets a constraint on the total household-level risk and balances farm-level and off-farm-level risk. Design/methodology/approach - The paper argues that the risk behaviour of farmers is better understood by considering risk at the household level. Using an analytical framework, equations are derived linking the farm activities, off-farm activities, consumption and business and private liquidity. Findings - The framework shows that a farm household that wants to minimize the risk that total household cash flow falls below consumption needs, may exhibit a wide variety of behavioural responses to changes in the policy and economic environment. Social implications - The framework suggests multiple ways for policy makers and individual farmers to support risk management. Originality/value - Risk management is at the core of the agricultural policy and it is of paramount importance to be able to understand behavioural responses to market and policy instruments. This paper contributes to that by suggesting that the focus of current risk analysis and management studies may be too narrowly focused at the farm level

Tropicalization of the moduli space of stable maps

Let $X$ be an algebraic variety and let $S$ be a tropical variety associated to $X$. We study the tropicalization map from the moduli space of stable maps into $X$ to the moduli space of tropical curves in $S$. We prove that it is a continuous map and that its image is compact and polyhedral. Loosely speaking, when we deform algebraic curves in $X$, the associated tropical curves in $S$ deform continuously; moreover, the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral. Our main tools are Berkovich spaces, formal models, balancing conditions, vanishing cycles and quantifier elimination for rigid subanalytic sets.Comment: I improved the theorems using parametrized tropical curves in Mathematische Zeitschrift, 201

Almost spanning subgraphs of random graphs after adversarial edge removal

Let Delta>1 be a fixed integer. We show that the random graph G(n,p) with p>>(log n/n)^{1/Delta} is robust with respect to the containment of almost spanning bipartite graphs H with maximum degree Delta and sublinear bandwidth in the following sense: asymptotically almost surely, if an adversary deletes arbitrary edges in G(n,p) such that each vertex loses less than half of its neighbours, then the resulting graph still contains a copy of all such H.Comment: 46 pages, 6 figure