FOURIER SPACE TIME-STEPPING ALGORITHM FOR VALUING GUARANTEED MINIMUM WITHDRAWAL BENEFITS IN VARIABLE ANNUITIES UNDER REGIME-SWITCHING AND STOCHASTIC MORTALITY

2017 ◽  
Vol 48 (1) ◽  
pp. 139-169 ◽  
Author(s):  
Katja Ignatieva ◽  
Andrew Song ◽  
Jonathan Ziveyi
Keyword(s):  
Regime Switching ◽  
Numerical Experiments ◽  
Space Time ◽  
Model Parameters ◽  
Percentage Increase ◽  
Fourier Space ◽  
Stochastic Mortality ◽  
Time Stepping ◽  
Force Of Interest ◽  
Stochastic Mortality Model

AbstractThis paper introduces the Fourier Space Time-Stepping algorithm to the valuation of variable annuity (VA) contracts embedded with guaranteed minimum withdrawal benefit (GMWB) riders when the underlying fund dynamics evolve under the influence of a regime-switching model. Mortality risk is introduced to the valuation framework by incorporating a two-factor affine stochastic mortality model proposed in Blackburn and Sherris (2013). The paper considers both, static and dynamic policyholder withdrawal behaviour associated with GMWB riders and assesses how model parameters influence the fees levied on providing such guarantees. Our numerical experiments reveal that the GMWB fees are very sensitive to regime-switching parameters; a percentage increase in the force of interest results in significant decrease in guarantee fees. The guarantee fees increase substantially with increasing volatility levels. Numerical experiments also highlight an increasing importance of mortality as maturity of the VA contract increases. Mortality has less impact on shorter maturity contracts regardless of the policyholder's withdrawal behaviour. As much as mortality influences pricing results for long maturities, the associated guarantee fees are decreasing functions of maturities for the VA contracts. Robustness checks of the Fourier Space Time-Stepping algorithm are performed by making numerical comparisons with several existing valuation approaches.

Fourier space time-stepping for option pricing with Lévy models

2008 ◽  
Vol 12 (2) ◽  
pp. 1-29 ◽  
Author(s):  
Kenneth Jackson ◽  
Sebastian Jaimungal ◽  
Vladimir Surkov
Keyword(s):  
Option Pricing ◽  
Space Time ◽  
Fourier Space ◽  
Time Stepping

scholarly journals A Square-Root Factor-Based Multi-Population Extension of the Mortality Laws

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2402
Author(s):  
Petar Jevtić ◽  
Luca Regis
Keyword(s):  
Maximum Likelihood ◽  
Model Parameters ◽  
Time Varying ◽  
Square Root ◽  
Stochastic Mortality ◽  
Mortality Model ◽  
Model Based ◽  
Males And Females ◽  
Quasi Maximum Likelihood ◽  
Stochastic Mortality Model

In this paper, we present and calibrate a multi-population stochastic mortality model based on latent square-root affine factors of the Cox-Ingersoll and Ross type. The model considers a generalization of the traditional actuarial mortality laws to a stochastic, multi-population and time-varying setting. We calibrate the model to fit the mortality dynamics of UK males and females over the last 50 years. We estimate the optimal states and model parameters using quasi-maximum likelihood techniques.

Fourier Space Time-Stepping for Option Pricing With Levy Models

2007 ◽  
Author(s):  
Kenneth R. Jackson ◽  
Sebastian Jaimungal ◽  
Vladimir Surkov
Keyword(s):  
Option Pricing ◽  
Space Time ◽  
Fourier Space ◽  
Time Stepping

scholarly journals СOMPUTER MODELING PARAMETERS OF TECHNOGENIC EMERGENCY SITUATIONS ON ENGINEERING INFRASTRUCTURE OF THE MEGAPOLIS

2021 ◽  
Vol 1 (1) ◽  
pp. 66-77
Author(s):  
M. V. Novozhylova ◽  
V. A. Andronov ◽  
R. S. Melezhik
Keyword(s):  
Time Series ◽  
Simulation Model ◽  
Numerical Experiments ◽  
Integrated Approach ◽  
Space Time ◽  
Comparative Statics ◽  
Information Support ◽  
Data Series ◽  
Model Parameters ◽  
Component Distribution

Context. The urgency of the research is to develop methods for analyzing and processing space-time information, namely the set of data distributed both in space and time and creating on this basis a computer probabilistic model of the process of predicting manmade emergencies on city engineering infrastructure. The spatio-temporal nature of data series causes additional requirements for the identification procedures of the mathematical model of a series, therefore, the number of approaches identifying its structure and construction of a series model has been proposed. Objective is methodical and software implementation of a computer model of the space-time series being intended to predict the future values of locations and times of man-made emergencies on the engineering infrastructure of the metropolis and increase decision-making efficiency. Method. A projection approach providing independent determination of random spatial parameters defining location of emergency units on engineering infrastructure as a sequence of two one-dimensional uniform distributions and describing time distribution of moments of accidents as non-stationary Poisson distribution has been developed. Proposed is an integrated approach which includes the construction of generator points, the power of which (characteristic of the accident complexity) based on the implementation of the comparative statics approach with so-called cumulative effect within a certain time. A relaxation approach based on the reduction of a two-dimensional simulation model of determining the city of possible emergency location to a set of independent onedimensional non-stationary (including stationary) distributions to generate the time of occurrence has been constructed. Formalization of the space-time field, procedures of information support of the process of forecasting the parameters of a possible emergency, typification of initial data for numerical experiments on the implementation of methods for forecasting the parameters of a possible emergency on the example of water supply and sewerage network of utility company Kharkivvodokal, city Kharkiv have been developed. Results. A dual methodology to determine the simulation model parameters of the space-time series, which contains both projection and integral approaches, as well as a combined method − relaxation approach, have been proposed. Numerical experiments based on the constructed model were performed. The model being considered is the theoretical basis to construct the forecast using a large amount of historical data. Conclusions. The method to predict the parameters of space-time series considering the nonstationarity property of the time component distribution has been further developed. Using the proposed computer simulation tools allows to increase the accuracy of the forecast of the location, time of occurrence and severity of a possible accident on the engineering infrastructure of the metropolis. 

scholarly journals Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1610
Author(s):  
Katia Colaneri ◽  
Alessandra Cretarola ◽  
Benedetta Salterini
Keyword(s):  
Stock Prices ◽  
Regime Switching ◽  
Common Factor ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Investment Strategy

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

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