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作者 Pham, Uyen Hoang
書名 Contributions to statistical analysis of financial risks
國際標準書號 9781124215075
book jacket
說明 239 p
附註 Source: Dissertation Abstracts International, Volume: 71-10, 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 non-arbitrage 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 Black-Scholes' 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 Black-Scholes' 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 decision-makers, we complete some preliminary work in the literature concerning how risk modeling should be related to utilities of decision-makers. 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 M-estimators and L-estimators. (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 heavy-tailed distributions
School code: 0143
Host Item Dissertation Abstracts International 71-10B
主題 Applied Mathematics
Economics, Finance
0364
0508
Alt Author New Mexico State University
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