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Polynomial processes and their applications to mathematical finance. (English) Zbl 1270.60079
The authors introduce a class of Markov processes, called polynomial processes (or \(m\)-polynomial processes), which have the property that the expected value of any polynomial of the random variable \(X_t\), \(t\geq 0\), is again a polynomial in the initial value of the process, meaning that moments of all orders of \(X_T\) can be computed in an easy and efficient way (even without probability distribution or characteristic function).
It is shown that this class of processes contains exponential Lévy processes, affine processes and processes of Pearson diffusion type. These processes can be applied, e.g., to GMM estimation procedures and to new techniques for option pricing and hedging. In particular, it can be also applied to variance reduction techniques in Monte Carlo methods due to the efficient and easy computation of moments.

MSC:
60J25 Continuous-time Markov processes on general state spaces
91B70 Stochastic models in economics
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