Malliavin Derivative for the Unknown Parameter in surplus process with mixed fractional Brownian motion
Chunhao Cai, Yingzhong Huang
TL;DR
This paper develops Malliavin calculus tools for mixed fractional Brownian motion with H > 1/2 and applies them to estimate the drift parameter in surplus processes driven by this noise.
Contribution
It introduces the Malliavin derivative and stochastic integral for mixed fractional Brownian motion and applies these to parameter estimation in surplus models.
Findings
Constructed Malliavin derivative for mfbm with H > 1/2
Developed stochastic integral with respect to mfbm
Applied to estimate drift parameter in surplus process
Abstract
In this paper, we will construct the Malliavin derivative and the stochastic integral with respect to the Mixed fractional Brownian motion (mfbm) for H > 1/2. As an application, we try to estimate the drift parameter via Malliavin derivative for surplus process with mixed fractional Brownian motion
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Complex Systems and Time Series Analysis