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arXiv · 1701.01238

Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility

Meriem Bel Hadj Khlifa·Yuliya Mishura·Kostiantyn Ralchenko·Mounir Zili
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Abstract

We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove existence--uniqueness results for weak and strong solutions of this equation under various conditions on the process $Y$ and the coefficients $a$, $\sigma_1$, and $\sigma_2$. Also, we study the strong consistency of the maximum likelihood estimator for the unknown parameter $\theta$. We suppose that $Y$ is in turn a solution of some diffusion SDE. Several examples of the main equation and of the process $Y$ are provided supplying the strong consistency.

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Meriem Bel Hadj Khlifa, Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili. 2017-01-05. Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility. https://doi.org/10.15559/16-vmsta66

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