Diffusion approximations in collective risk theory

Collective risk theory concerned with random fluctuations of total assets of insurance compan

Self-similar models in risk theory

This Ph.D. thesis is concerned with self-similar processes. In Chapter 2 we describe the classes of transformations leading from self-similar to stationary processes, and conversely. The relationship is used in Chapter 3 to characterize stable symmetric self-similar processes via their minimal integral representation. This leads to a unique decomposition of a symmetric stable self-similar process into three independent parts. The class of such processes appears to be quite broad and can stand as a basis of different risk models. In Chapter 4 we give examples of applications of self-similar processes in insurance risk modelling. In Chapter 5 we illustrate a test of self-similarity (namely variance-time plots) on DJIA index data in order to justify the use of self-similar processes in financial modelling. Last but not least we propose an alternative model for stock price movements incorporating a martingale which generates the same filtration as fractional Brownian motion.Self-similar process; Risk theory; Lamperti transformation; Insurance; Option pricing;

Risk Theory

[no abstract available

Endogenous technology adoption under production risk: theory and application to irrigation technology

The use of modern irrigation technologies has been proposed as one of several possible solutions to the problem of water resource scarcity and environmental degradation in many agricultural areas around the world. The main objective of this paper is to present a theoretical framework that conceptualizes adoption as a decision process involving information acquisition by farmers who face yield uncertainty and vary in their risk preferences. This is done by integrating the microeconomic foundations used to analyze production uncertainty at the farm level with the traditional technological adoption models. First we follow the approach of Antle (1987) based on higher-order moments of profit, which enables flexible estimation of the stochastic technology without ad hoc specification of risk preferences. Then individual risk preferences are derived, which are then used to explain farmer’s decision to adopt modern water saving technologies. The proposed model is applied to a randomly selected sample of 265 farms located in Crete, Greece. Results show that risk preferences affect the probability of adoption and provide evidence that farmers invest in new technologies as a means to hedge against input related production risk

Generalized Batch Normalization: Towards Accelerating Deep Neural Networks

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non-linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices.Comment: accepted at AAAI-1