scholarly journals Hattendorff Differential Equation for Multi-State Markov Insurance Models

Risks ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 169
Author(s):  
Rajeev Rajaram ◽  
Nathan Ritchey
Keyword(s):  
Differential Equation ◽  
Time Evolution ◽  
Discrete Time ◽  
Random Variable ◽  
The State ◽  
Numerical Computations ◽  
Matrix Notation ◽  
Insurance Model

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j, for a multistate Markov insurance model (denoted by 2σt(j)). We also show using matrix notation that both models can be easily adapted for use in MATLAB for numerical computations.

scholarly journals Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

2021 ◽  
Author(s):  
Nathan Ritchey ◽  
Rajeev Rajaram
Keyword(s):  
Differential Equation ◽  
Time Evolution ◽  
Continuous Time ◽  
Numerical Solutions ◽  
Random Variable ◽  
The State ◽  
Numerical Results ◽  
State Process ◽  
Differential Equa

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

scholarly journals Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

2021 ◽  
Author(s):  
Nathan Ritchey ◽  
Rajeev Rajaram
Keyword(s):  
Differential Equation ◽  
Time Evolution ◽  
Continuous Time ◽  
Numerical Solutions ◽  
Random Variable ◽  
The State ◽  
Numerical Results ◽  
State Process ◽  
Differential Equa

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

Static Instability of a Restrained Cantilever Column with a Tip Mass Subjected to a Subtangential Follower Force

2013 ◽  
Vol 345 ◽  
pp. 341-344
Author(s):  
Zhen Chao Su ◽  
Yan Xia Xue
Keyword(s):  
Differential Equation ◽  
Mass Parameter ◽  
Follower Force ◽  
Force Parameter ◽  
Euler Beam ◽  
Numerical Computations ◽  
Divergence Instability ◽  
Static Instability ◽  
Tip Mass

Based on the theory of Bernoulli-Euler beam, the differential equation of a restrained cantilever column with a tip mass subjected to a subtangential follower force is constructed, the solution of the differential equation is found, and the existence of regions of divergence instability of the system is discussed. The influence of the follower force parameter η, the tip mass parameter β and an end elastic end support on the divergence instability of the column is investigated. Several numerical computations of some cases have completed.

Derivation of a Differential Equation Exhibiting Replicative Time-Evolution Patterns by Inverse Ultra-Discretization

2009 ◽  
Vol 78 (3) ◽  
pp. 034002 ◽  
Author(s):  
Hiroshi Tanaka ◽  
Asumi Nakajima ◽  
Akinobu Nishiyama ◽  
Tetsuji Tokihiro
Keyword(s):  
Differential Equation ◽  
Time Evolution

scholarly journals Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process

2019 ◽  
Vol 29 (1) ◽  
pp. 135-144
Author(s):  
James Kim ◽  
Mohan Chaudhry ◽  
Abdalla Mansur
Keyword(s):  
Discrete Time ◽  
Renewal Process ◽  
Generating Functions ◽  
Continuous Time ◽  
Constant Term ◽  
Numerical Results ◽  
Asymptotic Results ◽  
Numerical Computations ◽  
Second Moments ◽  
Simplified Solution

This paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishable compared to those previously published where the constant term in the second moment is generated. In similar studies published in the literature, the constant term is either missing or not clear how it was obtained. The problem was partially solved in the study by Chaudhry and Fisher where they provided a asymptotic results for the non-bulk renewal density and for both the first and second moments using the generating functions. The objective of this work is to extend their results to the bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results.

Sign in / Sign up

Export Citation Format

Share Document