Journal ArticleDOI
The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
TLDR
In this article, the authors considered continuous-time counterparts of Z and S, and derived the distribution of ∫ exp(γt-σWt )1(0, ∞) (t)dt when W is Brownian motion.Abstract:
If Vk is the discount factor for the kth period, then Z = Σ k⩾1V 1...Vk Ck is the discounted value of a perpetuity paying Ck at time k. In some cases Z is also the limiting distribution of St =Vt (St-1 +Ct-1 ). This paper 1. reviews the literature concerning Z and {St } 2. considers continuous-time counterparts of Z and S, at the same time deriving the distribution of ∫ exp(-γt-σWt )1(0, ∞) (t)dt when W is Brownian motion; 3. gives applications to risk theory and pension funding.read more
Citations
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Journal ArticleDOI
Modelling Extremal Events for Insurance and Finance
TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.
Journal ArticleDOI
Bessel Processes, Asian Options, and Perpetuities
Hélyette Geman,Marc Yor +1 more
TL;DR: In this article, the Laplace transform of an Asian option which is out of the money is used to compute the moments of all orders of an arithmetic average of geometric Brownian motion, and a simple closed-form expression of the Asian option price when the option is "in the money".
Journal ArticleDOI
The concept of comonotonicity in actuarial science and finance: applications
TL;DR: In this article, the concept of Comonotonicity in actuarial science and finance has been used to derive approximations for sums of random variables, when the distributions of the components are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with.
Posted Content
The Concept of Comonotonicity in Actuarial Science and Finance: Applications
TL;DR: The concept of Comonotonicity in actuarial science and finance has been studied in this paper, where the authors derived approximations for sums of random variables, when the distributions of the components are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with.
Journal ArticleDOI
A survey and some generalizations of Bessel processes
Anja Göing-Jaeschke,Marc Yor +1 more
TL;DR: In this article, the first hitting times of squared Bessel processes and radial Ornstein-Uhlenbeck processes with negative dimensions or negative starting points are studied. But the authors focus on the first time a Bessel process hits a given barrier.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.