38 citations · 44 across the 17 of their papers we have counts for
22 papers
Cascade equation for the discontinuities in the Stefan problem with surface tension
Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has…
Optimal contract design via relaxation: application to the problem of brokerage fee for a client with private signal
Guillermo Alonso Alvarez, Sergey Nadtochiy
In this paper we show how the relaxation techniques can be used to establish the existence of an optimal contract in presence of information asymmetry. The method we illustrate was…
Stefan problem with surface tension: uniqueness of physical solutions under radial symmetry
Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov
We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite th…
Optimal brokerage contracts in Almgren-Chriss model with multiple clients
Guillermo Alonso Alvarez, Sergey Nadtochiy, Kevin Webster
This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren-Chriss model. The distinctive features…
Stefan problem with surface tension: global existence of physical solutions under radial symmetry
Sergey Nadtochiy, Mykhaylo Shkolnikov
We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the…
Consistency of MLE for partially observed diffusions, with application in market microstructure modeling
Sergey Nadtochiy, Yuan Yin
This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationa…
Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem
Sergey Nadtochiy, Mykhaylo Shkolnikov, Xiling Zhang
We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11],…
Reflected BSDEs in non-convex domains
Jean-François Chassagneux, Sergey Nadtochiy, Adrien Richou
This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped propert…
A simple microstructural explanation of the concavity of price impact
Sergey Nadtochiy
This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is mad…
Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact
Ibrahim Ekren, Sergey Nadtochiy
In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical cha…
Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness
Francois Delarue, Sergey Nadtochiy, Mykhaylo Shkolnikov
We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to defi…
Mean field systems on networks, with singular interaction through hitting times
Sergey Nadtochiy, Mykhaylo Shkolnikov
Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In co…
Optimal contract for a fund manager, with capital injections and endogenous trading constraints
Sergey Nadtochiy, Thaleia Zariphopoulou
In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in…
Control-stopping Games for Market Microstructure and Beyond
Roman Gayduk, Sergey Nadtochiy
In this paper, we present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic…
Particle systems with singular interaction through hitting times: application in systemic risk modeling
Sergey Nadtochiy, Mykhaylo Shkolnikov
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a l…
Robust Trading of Implied Skew
Sergey Nadtochiy, Jan Obloj
In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated impl…
Endogenous Formation of Limit Order Books: Dynamics Between Trades
Roman Gayduk, Sergey Nadtochiy
In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by ou…
Liquidity Effects of Trading Frequency
Roman Gayduk, Sergey Nadtochiy
In this article, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple…
Simulation of Implied Volatility Surfaces via Tangent Levy Models
Rene Carmona, Yi Ma, Sergey Nadtochiy
In this paper, we implement and test two types of market-based models for European-type options, based on the tangent Levy models proposed recently by R. Carmona and S. Nadtochiy.…
Local Variance Gamma and Explicit Calibration to Option Prices
Peter Carr, Sergey Nadtochiy
In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with mult…
Optimal investment for all time horizons and Martin boundary of space-time diffusions
Sergey Nadtochiy, Michael Tehranchi
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple tim…
Weak reflection principle for Lévy processes
Erhan Bayraktar, Sergey Nadtochiy
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the margin…