arXiv subjects

Artur Sidorenko

Publications and source records attributed to Artur Sidorenko.

5 recordsLinked to original sources

arXiv2026

Weighted derivative estimates for Kolmogorov equations

For diffusions whose coefficients are smooth, with at most linear growth and bounded derivatives of higher order, we establish explicit pointwise bounds on the spatial derivatives of the classical solution to the Cauchy problem with polynomially growing initial data. We also obtain explicit growth estimates for the derivatives of the SDE with respect to the initial data. The proofs combine Lyapunov functions and Markov semigroups on weighted spaces with Kunita's theory of the differentiable dependence of SDE solutions on the initial data.

math.AP↗

arXiv2026

Convergence Rates of Continuous-Time Random Walks to Time-Fractional Diffusions with Unbounded Coefficients

We investigate uniform weak convergence rates for probabilistic numerical methods applied to backward time-fractional diffusion equations whose dynamics are driven by diffusions with possibly unbounded coefficients, such as the Geometric Brownian Motion. The fractional structure is represented through a random time-change by the inverse of a stable subordinator. To approximate the underlying fractional dynamics, we combine discrete Markov chain schemes for the diffusion component with heavy-tailed random walk approximations of the time change. Our analysis builds on Feller semigroup techniques and a high-order sensitivity framework for diffusion semigroups based on the Kunita stochastic flows and tensor fields. We derive uniform bounds for all orders of sensitivities, establish a quasi-contraction property for the associated semigroup, and transfer these estimates to the fractional setting via the convolution representation with the inverse subordinator. As a result, under killing conditions which dominate at least the base-space semigroup growth, we obtain weak convergence rates for the combined continuous-time-random-walk scheme to the time-fractional diffusion, with a logarithmic regime before the discount dominates the stronger smooth-space growth.

math.PR↗

arXiv2026

On convergence of the Mayer problems arising in the theory of financial markets with transaction cost

The geometric approach to financial markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by the two random processes, S and K. The first one, d-dimensional, models the price evolution of basic securities while the second one, cone-valued, describes the evolution of the solvency set. It happened that the fundamental questions -- no-arbitrage criteria, hedging problems, portfolio optimization -- can be studied in this general setting opening the door to set-valued techniques. In this note we explore, in such a general framework, the stochastic Mayer control problem, consisting in the maximization of the expected utility of the portfolio terminal wealth. We get results on continuity of the optimal value and the optimal control under price approximations in a general multi-asset framework described by the geometric formalism.

q-fin.MF↗

arXiv2025

Skorokhod Transition in the Conic Market Model

This paper examines the applicability of the Skorokhod representation theorem in filtrated probability spaces for the utility maximization problem in the Kabanov conic model of multi-asset markets with proportional transaction costs. A key challenge is that the theorem does not necessarily preserve adaptedness, meaning that solutions obtained on an auxiliary probability space may not correspond to those on the original one. We establish that, under mild conditions, the Bellman functionals remain consistent across different probability spaces.

math.PR↗

arXiv2025

Well-posedness of behavioral singular stochastic control problems

We investigate the well-posedness of a general class of singular stochastic control problems in which controls are processes of finite variation. We develop an abstract framework, which we then apply to storage management and portfolio investment problems under proportional transaction costs. Within this setting, we establish the existence of an optimal strategy in the class of randomized controls for a range of goal functionals, including cumulative prospect theory (CPT) preferences. To the best of our knowledge, this is the first treatment of behavioral storage management with the CPT goal functional. For the portfolio management problem, our analysis exploits the metrizable Meyer-Zheng topology to simplify proofs. We thoroughly investigate the applicability of the Skorokhod representation theorem for adapted random processes. Overall, the presented framework provides a clear separation between constraints imposed on the market model and properties required of the goal functional.

q-fin.MF↗