說明 
239 p 
附註 
Source: Dissertation Abstracts International, Volume: 7110, Section: B, page: 6208 

Adviser: Hung T. Nguyen 

Thesis (Ph.D.)New Mexico State University, 2010 

This research concerns theoretical foundations of financial risk modeling and its statistical aspects. Our main contributions are as follows. (i) A systematic study of Choquet integral as the most general form for modeling coherent risk measures, where, besides the popular and special case of distorted probability measures in actuarial science, we consider a broader framework of Choquet capacities in the context of the theory of random sets. (ii) The connection between pricing of derivative securities in complete markets (via the nonarbitrage principle) and premium calculations in actuarial science (via premium principles) is investigated leading to new results concerning martingale measures (via Girsanov's theorem and Esscher's transform) and distortion functions (via Choquet integral representation). These are first based upon the classic BlackScholes' model of diffusion processes, and then extended to Levy processes. (iii) Placing risk assessment within the context of financial economics, we investigate a recent claim on the consistency of risk evaluations with respect to time horizons. We validate this consistency in some popular models (the BlackScholes' models, two Levy processes, namely the shifted Poisson process and random walks). (iv) As financial risks depend not only on the loss random variables considered but also on the risk attitudes of the decisionmakers, we complete some preliminary work in the literature concerning how risk modeling should be related to utilities of decisionmakers. This is achieved by using a novel approach based upon robust statistics, in which we explore the concept of asymptotic equivalence of robust estimators such as Mestimators and Lestimators. (v) Having a class of reasonable risk measures, we proceed to examine various new statistical estimation problems. These include data driven methods, statistics with indirect observations, statistics with coarse (low quality, imprecise) data using a random set approach, as well as statistics with heavytailed distributions 

School code: 0143 
Host Item 
Dissertation Abstracts International 7110B

主題 
Applied Mathematics


Economics, Finance


0364


0508

Alt Author 
New Mexico State University

