FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE

By Yaozhong Hu, Bernt Øksendal. 2003

536 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/5e2f99f271e766b0ce1d3eeb334c32d67d89b580

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Citations in the corpus

An S-transform approach to integration with respect to a fractional Brownian motion (2003, methodology): “(1999), Hu and Oksendal (2003) and Elliott and van der Hoek (2003).”
Dynamical pricing of weather derivatives (2002, methodology): “Stochastic integrals with respect to an FBM with Hurst exponent H ∈ ( 12 , 1) of Itô type that have zero expectation have been introduced and studied by Duncan et al (2000), and Hu and Øksendal (1999) (see also Gripenberg and Norres 1996).”
Parameter estimation for fractional Ornstein–Uhlenbeck processes (2009, background): “where ∫ T 0 XtdB H t is a divergence-type integral (see [1], [3], [4], [7] and the references therein), and we call it the least squares estimator.”
Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008, background): “[8], Hu and Øksendal [9], and Cheridito and Nualart [10], among others.”
Statistical aspects of the fractional stochastic calculus (2006, background): “[18], [14]) and this motivates the statistical study of stochastic di erential equations governed by fBm.”
On arbitrage and replication in the fractional Black-Scholes pricing model (2003, methodology): “Let us note, however, that the proof of the freedom of arbitrage in [3, 8] does not assume that the portfolio is adapted to the filtration generated by the stock price process.”
Pricing Currency Option in a Mixed Fractional Brownian Motion with Jumps Environment (2014, unknown): “This outcome can be found in [45, 46, 53, 54].”
Dynamic models of long-memory processes driven by Lévy noise (2002, background): “Recently, Hu and Øksendal [37] have shown that fractional Black–Scholes markets offer no arbitrage if stochastic integrals with respect to FBM are defined via the Wick product.”
Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio (2010, background): “It is well known that the dynamics of fractal processes are very different depending upon whether they involve longrange dependence or short-range dependence [11,24], and fortunately we came across this property.”
Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, methodology): “Another important difference between the divergence integral in this paper and the stochastic integral of [15] and [4] is that the stochastic integral of divergence type in this paper is always a random variable whereas in [15] and [4], the stochastic integral is defined as a Hida distribution.”