Anton Yurchenko-Tytarenko

• Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2022). Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. doi: 10.1080/17442508.2022.2047188. Fulltekst i vitenarkiv
• Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2020). Approximating Expected Value of an Option with Non-Lipschitz Payoff in Fractional Heston-Type Model. International Journal of Theoretical and Applied Finance. ISSN 0219-0249. 23(5). doi: 10.1142/S0219024920500314. Fulltekst i vitenarkiv

Se alle arbeider i Cristin

• Nunno, Giulia Di & Yurchenko-Tytarenko, Anton (2021). Rough volatility: SDE with unbounded drift driven by Hölder continuous noise.
• Giordano, Michele & Yurchenko-Tytarenko, Anton (2021). Optimal control in linear stochastic advertising models with memory.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Volterra Sandwiched Volatility Model.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2021). Stochastic volatility modelling via sandwiched processes with Volterra noise.
• Nunno, Giulia Di; Mishura, Yuliya & Yurchenko-Tytarenko, Anton (2020). Approximating expected value of an option with non-Lipschitz payoff in fractional Heston-type model.
• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Hölder noises.
• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Holder noises.
• Yurchenko-Tytarenko, Anton (2020). Sandwiched processes driven by Hölder noises. Vis sammendrag

  We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above some continuous function or has continuous upper and lower bounds. Under some additional assumptions on the noise, we prove that the solution has moments of all orders. Additionally, numeric schemes for the solution are considered. As illustrations of our approach, generalised CIR and CEV processes will be discussed. This talk is based on joint work with Giulia Di Nunno and Yuliya Mishura.

• Yurchenko-Tytarenko, Anton (2020). SDEs with unbounded drift driven by Holder noises. Vis sammendrag

  In this research, we consider a stochastic differential equation with drift having singularity in zero and an additive noise being a fractional Brownian motion with an arbitrary Hurst parameter. Under some assumptions, existence, uniqueness and positivity of the solution are proved, finiteness of the moments of all orders (including the negative ones) is obtained. As examples, we provide fractional generalisations of the CIR and CEV processes and, using the finiteness of their negative moments, prove convergence of the corresponding backward Euler-type schemes. Separately, we discuss possible extensions of the obtained results including replacing the fractional Brownian motion with general Holder-continuous Volterra process.

Se alle arbeider i Cristin