Yaozhong Hu

Integral transformations and anticipative calculus for fractional Brownian motions

Introduction Representations Induced transformation I Approximation Induced transformation II Stochastic calculus of variation Stochastic integration Nonlinear translation (Absolute continuity) Conditional expectation Integration by parts Composition (Ito formula) Clark type representation Continuation Stochastic control Appendix Bibliography.

A Delayed Black and Scholes Formula

Abstract In this article we develop an explicit formula for pricing European options when the underlying stock price follows nonlinear stochastic functional differential equations with fixed and variable delays. We believe that the proposed models are sufficiently flexible to fit real market data, and yet simple enough to allow for a closed-form representation of the option price. Furthermore, the models maintain the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent local martingale measure.

Renormalized self-intersection local time for fractional brownian motion

Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Assume d ≥ 2. We prove that the renormalized self-intersection local time l=∫ T 0 ∫ t 0 δ(B H t - B H s )ds dt - E(∫ T 0 ∫ t 0 δ(B H t -B H s )ds dt) exists in L 2 if and only if H H ≥ 3 2d, r(e)l e converges in distribution to a normal law N(0, Tσ 2 ), as e tends to zero, where l e is an approximation of l, defined through (2), and r(e) = |loge| -1 if H = 3/(2d), and r(e) = e d-3/(2H) if 3/(2d) < H.

Optimal time to invest when the price processes are geometric Brownian motions

Abstract. Let

Feynman–Kac formula for heat equation driven by fractional white noise

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A stochastic maximum principle for processes driven by fractional Brownian motion

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OPTIMAL CONSUMPTION AND PORTFOLIO IN A BLACK–SCHOLES MARKET DRIVEN BY FRACTIONAL BROWNIAN MOTION

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Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities

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Stochastic Control for Linear Systems Driven by Fractional Noises

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Partial Information Linear Quadratic Control for Jump Diffusions

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