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Some recent progress on numerical methods for controlled regime-switching models with applications to insurance and risk management. (English) Zbl 1349.91308

Summary: 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.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
93B40 Computational methods in systems theory (MSC2010)
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