## A recursive approach to mortality-linked derivative pricing.(English)Zbl 1218.91156

Summary: We develop a recursive method to derive an exact numerical and nearly analytical representation of the Laplace transform of the transition density function with respect to the time variable for time-homogeneous diffusion processes. We further apply this recursion algorithm to the pricing of mortality-linked derivatives. Given an arbitrary stochastic future lifetime $$\mathbb T$$, the probability distribution function of the present value of a cash flow depending on $$\mathbb T$$ can be approximated by a mixture of exponentials, based on Jacobi polynomial expansions. In case of mortality-linked derivative pricing, the required Laplace inversion can be avoided by introducing this mixture of exponentials as an approximation of the distribution of the survival time $$\mathbb T$$ in the recursion scheme. This approximation significantly improves the efficiency of the algorithm.

### MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 65R10 Numerical methods for integral transforms 44A10 Laplace transform 91B30 Risk theory, insurance (MSC2010) 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60H30 Applications of stochastic analysis (to PDEs, etc.)
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