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2007

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Articles 1 - 9 of 9

Full-Text Articles in Probability

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang Dec 2007

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …


On The Total Duration Of Negative Surplus Of A Risk Process With Two-Step Premium Function, Pavlina Jordanova Dec 2007

On The Total Duration Of Negative Surplus Of A Risk Process With Two-Step Premium Function, Pavlina Jordanova

Applications and Applied Mathematics: An International Journal (AAM)

We consider a risk reserve process whose premium rate reduces from cd to cu when the reserve comes above some critical value v. In the model of Cramer-Lundberg with initial capital u ≥ 0, we obtain the probability that ruin does not occur before the first up-crossing of level v. When u < v, following H. Gerber and E. Shiu (1997), we derive the probability that starting with initial capital u ruin occurs and the severity of ruin is not bigger than v. Further we express the probability of ruin in the two step premium function model - ψ (u,v), by the last two probabilities. Our assumptions imply that the surplus process will go to infinity almost surely. This entails that the process will stay below zero only temporarily. We derive the distribution of the total duration of negative surplus and obtain its Laplace transform and mean value. As a consequence of these results, under certain conditions in the Model of Cramer-Lundberg we obtain the expected value of the severity of ruin. In the end of the paper we give examples with exponential claim sizes.


Radical Impact Of Change In Actions And Confidence Index On Reverse Decision Making An Application Based Study, Swatee Trimbak Paithankar Oct 2007

Radical Impact Of Change In Actions And Confidence Index On Reverse Decision Making An Application Based Study, Swatee Trimbak Paithankar

Engineering Management & Systems Engineering Theses & Dissertations

While making decisions under uncertainty, people are often unaware of the logical approach to form the decision process. It is assumed that collecting details, analyzing and evaluating data is enough to make 'proper' decisions. However, past research in the decision making arena has significantly validated that there exists a class of decision problems which is complex, ill-structured and not defined to the level where decision makers can draw logical conclusions based on existing traditional decision approaches. RDM (reverse decision making), one of the novel approaches of decision making under conditions of uncertainty, has shown potential towards addressing some of these …


The Shift From Defined Benefit Pensions To 401(K) Plans And The Pension Assets Of The Baby Boom Cohort, James Poterba, Steven Venti, David A. Wise Aug 2007

The Shift From Defined Benefit Pensions To 401(K) Plans And The Pension Assets Of The Baby Boom Cohort, James Poterba, Steven Venti, David A. Wise

Dartmouth Scholarship

The rise of 401(k) plans and the decline of defined benefit plans will have an important effect on the wealth of future retirees. Changing demographic structure also will affect the aggregate stock of retirement wealth. We project the stock of assets held in retirement plans and the average retirement saving of retirees through 2040. Our projections show large increases in wealth at retirement, especially if the returns on corporate equities are comparable with historical returns. Retirement wealth will grow, however, even if equity returns fall substantially below their historical level.


Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro Jan 2007

Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions.


A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia Jan 2007

A Distributed Parabolic Control With Mixed Boundary Conditions, Jose-Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion Γ1 of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control ĝα with optimal state uĝαα and optimal adjoint state pĝαα are convergent as α → 1 …


Why De Minimis?, Matthew D. Adler Jan 2007

Why De Minimis?, Matthew D. Adler

Faculty Scholarship

De minimis cutoffs are a familiar feature of risk regulation. This includes the quantitative individual risk thresholds for fatality risks employed in many contexts by EPA, FDA, and other agencies, such as the 1-in-1 million lifetime cancer risk cutoff; extreme event cutoffs for addressing natural hazards, such as the 100 - year - flood or 475 - year - earthquake; de minimis failure probabilities for built structures; the exclusion of low - probability causal models; and other policymaking criteria. All these tests have a common structure, as I show in the Article. A de minimis test, broadly defined, tells the …


First Passage Time Problem For Multivariate Jump-Diffusion Processes: Models, Computation, And Applications In Finance, Di Zhang Jan 2007

First Passage Time Problem For Multivariate Jump-Diffusion Processes: Models, Computation, And Applications In Finance, Di Zhang

Theses and Dissertations (Comprehensive)

The first passage time (FPT) problems are ubiquitous in many applications, from physics to finance. Mathematically, such problems are often reduced to the evaluation of the probability density of the time for a process to cross a certain level, a boundary, or to enter a certain region. While in other areas of applications the FPT problems can often be solved analytically, in finance we usually have to resort to the application of numerical procedures, in particular when we deal with jump-diffusion stochastic processes (JDP). The application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, …


Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo Jan 2007

Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo

Mathematics & Statistics Theses & Dissertations

Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …