APPROXIMATING THE DENSITY OF THE TIME TO RUIN VIA FOURIER-COSINE SERIES EXPANSION

Zhimin Zhang

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

Abstract In this paper, the density of the time to ruin is studied in the context of the classical compound Poisson risk model. Both one-dimensional and two-dimensional Fourier-cosine series expansions are used to approximate the density of the time to ruin, and the approximation errors are also obtained. Some numerical examples are also presented to show that the proposed method is very efficient.

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References

1998On the Time Value of Ruin 2008A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions 2009Pricing early-exercise and discrete barrier options by fourier-cosine series expansions 2000The moments of the time of ruin, the surplus before ruin, and the deficit at ruin 2012Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options 2007On the Class of Erlang Mixtures with Risk Theoretic Applications 2005The Density of the Time to Ruin in the Classical Poisson Risk Model 2013Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

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