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Stochastic Differential Equations: S...

Temple University.

Stochastic Differential Equations: Some Risk and Insurance Applications.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic Differential Equations: Some Risk and Insurance Applications.
作者:	Xiong, Sheng.
面頁冊數:	76 p.
附註:	Source: Dissertation Abstracts International, Volume: 72-08, Section: B, page: 4706.
附註:	Adviser: Wei-Shih Yang.
Contained By:	Dissertation Abstracts International72-08B.
標題:	Applied Mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3457962
ISBN:	9781124691176

Stochastic Differential Equations: Some Risk and Insurance Applications.
Xiong, Sheng.

Stochastic Differential Equations: Some Risk and Insurance Applications. - 76 p.

Source: Dissertation Abstracts International, Volume: 72-08, Section: B, page: 4706.

Thesis (Ph.D.)--Temple University, 2011.

In this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G &sube; Rd, and let Ut be a utility function of Xt with U 0 = u0. Let T be the first time that Ut reaches a level u*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psi(u0) = Pr {T < infinity}, and other important probabilities. A class of exponential martingales is constructed to analyze the asymptotic properties of all probabilities. In addition, we prove that the expected discounted penalty function, a generalization of the probability of ultimate ruin, satisfies an elliptic partial differential equation, subject to some initial boundary conditions. Two examples from areas of actuarial work to which martingales have been applied are given to illustrate our methods and results: 1. Insurer's insolvency. 2. Terrorism risk. In particular, we study insurer's insolvency for the Cramer-Lundberg model with investments whose price follows a geometric Brownian motion. We prove the conjecture proposed by Constantinescu and Thommann.

ISBN: 9781124691176Subjects--Topical Terms:

530992
Applied Mathematics.

Stochastic Differential Equations: Some Risk and Insurance Applications.
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520 $a In this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G &sube; Rd, and let Ut be a utility function of Xt with U 0 = u0. Let T be the first time that Ut reaches a level u*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psi(u0) = Pr {T < infinity}, and other important probabilities. A class of exponential martingales is constructed to analyze the asymptotic properties of all probabilities. In addition, we prove that the expected discounted penalty function, a generalization of the probability of ultimate ruin, satisfies an elliptic partial differential equation, subject to some initial boundary conditions. Two examples from areas of actuarial work to which martingales have been applied are given to illustrate our methods and results: 1. Insurer's insolvency. 2. Terrorism risk. In particular, we study insurer's insolvency for the Cramer-Lundberg model with investments whose price follows a geometric Brownian motion. We prove the conjecture proposed by Constantinescu and Thommann.
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