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Contributions to statistical analysi...

Pham, Uyen Hoang.

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Contributions to statistical analysis of financial risks.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Contributions to statistical analysis of financial risks./
作者:	Pham, Uyen Hoang.
面頁冊數:	239 p.
附註:	Source: Dissertation Abstracts International, Volume: 71-10, Section: B, page: 6208.
Contained By:	Dissertation Abstracts International71-10B.
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3424316
ISBN:	9781124215075

Contributions to statistical analysis of financial risks.
Pham, Uyen Hoang.

Contributions to statistical analysis of financial risks. - 239 p.

Source: Dissertation Abstracts International, Volume: 71-10, Section: B, page: 6208.

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.

ISBN: 9781124215075Subjects--Topical Terms:

1669109
Applied Mathematics.

Contributions to statistical analysis of financial risks.
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