Some Recent Progress on Numerical Methods for Controlled Regime-Switching Models with Applications to Insurance and Risk Management
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Zhuo Jin
,
Rebecca Stockbridge
Abstract
This paper provides a survey on several numerical approximation schemes for stochastic control problems that arise from actuarial science and finance. The problems to be considered include dividend optimization, reinsurance game, and quantile hedging for guaranteed minimum death benefits. To better describe the complicated financial markets and their inherent uncertainty and randomness, the so-called regime-switching models are adopted. Such models are more realistic and versatile, however, far more complicated to handle. Due to the complexity of the construction, the regime-switching diffusion systems can only be solved in very special cases. In general, it is virtually impossible to obtain closed-form solutions. We use Markov chain approximation techniques to construct discrete-time controlled Markov chains to approximate the value function and optimal controls. Examples are presented to illustrate the applicability of the numerical methods.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1207667
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Numerical Simulation of Surface Acoustic Wave Actuated Separation of Rigid Enantiomers by the Fictitious Domain Lagrange Multiplier Method
- An Optimal Adaptive Finite Element Method for an Obstacle Problem
- On ℓ1-Regularization in Light of Nashed's Ill-Posedness Concept
- Shape Optimization by Pursuing Diffeomorphisms
- Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems
- Some Recent Progress on Numerical Methods for Controlled Regime-Switching Models with Applications to Insurance and Risk Management
- Functional A Posteriori Error Estimates for Parabolic Time-Periodic Boundary Value Problems
- M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator
- Dual Weighted Residual Error Control for Frictional Contact Problems
Articles in the same Issue
- Frontmatter
- Numerical Simulation of Surface Acoustic Wave Actuated Separation of Rigid Enantiomers by the Fictitious Domain Lagrange Multiplier Method
- An Optimal Adaptive Finite Element Method for an Obstacle Problem
- On ℓ1-Regularization in Light of Nashed's Ill-Posedness Concept
- Shape Optimization by Pursuing Diffeomorphisms
- Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems
- Some Recent Progress on Numerical Methods for Controlled Regime-Switching Models with Applications to Insurance and Risk Management
- Functional A Posteriori Error Estimates for Parabolic Time-Periodic Boundary Value Problems
- M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator
- Dual Weighted Residual Error Control for Frictional Contact Problems
