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This article presents a flood risk analysis model that considers the spatially heterogeneous nature of flood events. The basic concept of this approach is to generate a large sample of flood events that can be regarded as temporal extrapolation of flood events. These are combined with cumulative flood impact indicators, such as building damages, to finally derive time series of damages for risk estimation. Therefore, a multivariate modeling procedure that is able to take into account the spatial characteristics of flooding, the regionalization method top-kriging, and three different impact indicators are combined in a model chain. Eventually, the expected annual flood impact (e.g., expected annual damages) and the flood impact associated with a low probability of occurrence are determined for a study area. The risk model has the potential to augment the understanding of flood risk in a region and thereby contribute to enhanced risk management of, for example, risk analysts and policymakers or insurance companies. The modeling framework was successfully applied in a proof-of-concept exercise in Vorarlberg (Austria). The results of the case study show that risk analysis has to be based on spatially heterogeneous flood events in order to estimate flood risk adequately.

We present simple examples of (competitive) two species systems with complicated dynamic behaviour. From almost all initial conditions one of the two species dies out. But the survivor is unpredictable: The basins of the two chaotic one-species attractors are everywhere dense and intermingled.

Flooding often has a negative impact on society. In particular, widespread flood events can cause a lot of damage. These events are often spatially and temporally heterogeneous and should be duly considered for an appropriate analysis of flooding. Therefore, a conditional multivariate approach is adapted and applied in order to (i) contribute to a better understanding of the spatial characteristics of fluvial floods and (ii) to deliver sets of synthetically generated flood events. The present paper focuses on a simulation procedure consisting of careful data preparation and selection and the application of a conditional multivariate approach. The conditional approach is adapted to account for the seasonality of runoff data. Model checks attuned to the model are presented to ensure the consistence of simulated and observed data. The Austrian Province Vorarlberg was chosen as the study area. A thorough data analysis of runoff time series showed that the hydrological behaviour is characterized by a strong seasonality that was considered within the applied modelling procedure. The analysis of the spatial dependence of high river flows identified regions where floods likely occur simultaneously and regions with low spatial dependence. The main result of the modelling procedure, a large set of widespread flood events, was successfully generated.

A class of transformations on $[0,1]^2$, which includes transformations obtained by a Poincaré section of the Lorenz equation, is considered. We prove a formula which connects local dimension, entropy and characteristic exponents of ergodic invariant probability measures.

This paper suggests a resolution to what has come to be known as the 'private equity premium puzzle' (Am. Econom. Rev. 92(4) (2002) 745-778). We interpret occupational choice as a dynamic portfolio choice problem of a life-cycle investor facing a borrowing constraint, stock market participation costs and imperfect information about the profitability of potential businesses. Information is imperfect, because only entrepreneurs observe their own business risk realizations and there is a fixed cost of starting a business. Using numerical techniques we find that the model generates the empirically observed return structure for private and public equity with standard CRRA-preferences and fully rational expectations. r 2004 Elsevier B.V. All rights reserved. JEL classification: G11; D91

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This paper suggests a solution to what has become known as the "private equity premium puzzle" (Moskowitz and Vissing-Jorgensen (2002)). We interpret occupational choice as a dynamic portfolio choice problem of a life-cycle investor facing a liquidity constraint and imperfect information about the profitability of potential businesses. In this setting, becoming an entrepreneur is equivalent to investing in non-traded private equity capital subject to transaction costs. We model the return on private equity as the sum of two components, the individual ability of the entrepreneur and idiosyncratic business risk. Information is imperfect, because only entrepreneurs observe their own business risk realizations. Using numerical techniques we find that the model generates the observed return structure for private equity using standard CRRA-preferences and fully rational expectations.