scholarly journals Time-dynamic evaluations under non-monotone information generated by marked point processes

2021 ◽  
Author(s):  
Marcus C. Christiansen
Keyword(s):  
General Theory ◽  
Life Insurance ◽  
Point Processes ◽  
Marked Point ◽  
Information Loss ◽  
Marked Point Processes ◽  
Central Idea ◽  
Information Dynamics ◽  
Time Dynamic ◽  
Short Intervals

AbstractThe information dynamics in finance and insurance applications is usually modelled by a filtration. This paper looks at situations where information restrictions apply so that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale representations. We present a general theory that extends classical martingale representations to non-monotone information generated by marked point processes. The central idea is to focus only on those properties that martingales and compensators show on infinitesimally short intervals. While classical martingale representations describe innovations only, our representations have an additional symmetric counterpart that quantifies the effect of information loss. We exemplify the results with examples from life insurance and credit risk.

Unit-Linked Life Insurance Contracts with Lapse Rates Dependent on Economic Factors

2006 ◽  
Vol 1 (1) ◽  
pp. 49-78 ◽  
Author(s):  
A. W. Kolkiewicz ◽  
K. S. Tan
Keyword(s):  
Financial Markets ◽  
Life Insurance ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes ◽  
Economic Factors ◽  
Insurance Contracts ◽  
Insurance Policies ◽  
Strong Relation ◽  
Lapse Rates

ABSTRACTMany recently introduced unit-linked life insurance policies contain provisions allowing policyholders to lapse the product. The problem of pricing this surrender option is difficult as it involves modelling lapse decisions which may be contingent on different factors. This paper develops a methodology which enables us to model lapse behaviour within a framework provided by developments in financial economics. Using marked point processes with stochastic intensities, we present an approach which accounts for changes in the lapse behaviour of policyholders due to different economic factors. As a result, the model produces more accurate financial values for insurance contracts contingent on financial markets. In the context of unit-linked policies, we illustrate the method by allowing the lapse decision to depend on the stochastic volatility of the underlying asset. Our simulation study indicates that there is a strong relation between the single premiums of these policies and the lapse behaviour.

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (02) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Some EATA properties for marked point processes

1995 ◽  
Vol 32 (04) ◽  
pp. 922-929
Author(s):  
D. Kofman ◽  
H. Korezlioglu
Keyword(s):  
Point Processes ◽  
Stochastic Integral ◽  
Marked Point ◽  
Marked Point Processes ◽  
Batch Arrival ◽  
Integral Approach ◽  
Arrival Processes

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

Integral equations for compound distribution functions

1996 ◽  
Vol 33 (2) ◽  
pp. 388-399 ◽  
Author(s):  
Christian Max Møller
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Building Blocks ◽  
Distribution Functions ◽  
Jump Processes ◽  
Marked Point Processes ◽  
Martingale Theory ◽  
Compound Distribution ◽  
Change Of Variable ◽  
Fixed Period

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.

Sign in / Sign up

Export Citation Format

Share Document