• Corpus ID: 251041084

# Phase-type representations of stochastic interest rates with applications to life insurance

```@inproceedings{Ahmad2022PhasetypeRO,
title={Phase-type representations of stochastic interest rates with applications to life insurance},
year={2022}
}```
• Published 22 July 2022
• Mathematics
. The purpose of the present paper is to incorporate stochastic interest rates into a matrix–approach to multi–state life insurance, where formulas for reserves, moments of future payments and equivalence premiums can be obtained as explicit formulas in terms of product integrals or matrix exponentials. To this end we consider the Markovian interest model, where the rates are piecewise deterministic (or even constant) in the diﬀerent states of a Markov jump process, and which is shown to…

## References

SHOWING 1-10 OF 28 REFERENCES

• Mathematics
European Actuarial Journal
• 2020
A multi-state life insurance model is described naturally in terms of the intensity matrix of an underlying (time-inhomogeneous) Markov process which specifies the dynamics for the states of an
The main purpose of this work is to derive a partial differential equation for the reserves of life insurance liabilities subject to stochastic interest rates where the benefits and premiums depend
The force of interest is modelled by a homogeneous time-continuous Markov chain with finite state space. Ordinary differential equations are obtained for expected values of various functionals of
1. A general life insurance model.- 2. Stochastic processes.- 3. Interest rate.- 4. Cash flows and the mathematical reserve.- 5. Difference equations and differential equations.- 6. Examples and
• Economics
European Actuarial Journal
• 2019
We consider two aspects of Vasicek interest rate models arising from chance-risk classification of German pension products. First, we show that the two-factor Vasicek model can explain significantly
• Mathematics
• 1996
Abstract The classical Thiele's differential equation for the prospective reserve of an insurance policy has been generalized to models with counting process driven payments and deterministic
• Economics
• 2001
Basic Definitions and No Arbitrage.- Definitions and Notation.- No-Arbitrage Pricing and Numeraire Change.- From Short Rate Models to HJM.- One-factor short-rate models.- Two-Factor Short-Rate
• Economics
Scandinavian Actuarial Journal
• 2020
We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are
Prospective and retrospective reserves are defined as conditional expected values, given some information available at the time of consideration. Each specification of the information invoked gives