13 citations · 30 across the 14 of their papers we have counts for
16 papers
On convergence of forecasts in prediction markets
Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin
We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correc…
Optimal growth strategies for a representative agent in a continuous-time asset market
Mikhail Zhitlukhin
We propose a multi-agent model of an asset market and study conditions that guarantee that the strategy of an individual agent cannot outperform the market. The model assumes a mea…
Asymptotically optimal strategies in a diffusion approximation of a repeated betting game
Mikhail Zhitlukhin
We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal…
Capital growth and survival strategies in a market with endogenous prices
Mikhail Zhitlukhin
We call an investment strategy survival, if an agent who uses it maintains a non-vanishing share of market wealth over the infinite time horizon. In a discrete-time multi-agent mod…
A continuous-time asset market game with short-lived assets
Mikhail Zhitlukhin
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stocha…
A sequential test for the drift of a Brownian motion with a possibility to change a decision
Mikhail Zhitlukhin
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initia…
Asymptotic minimization of expected time to reach a large wealth level in an asset market game
Mikhail Zhitlukhin
We consider a stochastic game-theoretic model of a discrete-time asset market with short-lived assets and endogenous asset prices. We prove that the strategy which invests in the a…
Sequential tracking of an unobservable two-state Markov process under Brownian noise
Alexey Muravlev, Mikhail Urusov, Mikhail Zhitlukhin
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-…
Relative growth optimal strategies in an asset market game
Yaroslav Drokin, Mikhail Zhitlukhin
We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of…
Survival investment strategies in a continuous-time market model with competition
Mikhail Zhitlukhin
We consider a stochastic game-theoretic model of an investment market in continuous time with short-lived assets and study strategies, called survival, which guarantee that the rel…
Monotone Sharpe ratios and related measures of investment performance
Mikhail Zhitlukhin
We introduce a new measure of performance of investment strategies, the monotone Sharpe ratio. We study its properties, establish a connection with coherent risk measures, and obta…
A Bayesian sequential test for the drift of a fractional Brownian motion
Alexey Muravlev, Mikhail Zhitlukhin
We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesi…
On the maximum of discretely sampled fractional Brownian motion with small Hurst parameter
Konstantin Borovkov, Mikhail Zhitlukhin
We show that the distribution of the maximum of the fractional Brownian motion with Hurst parameter over an -point set can be approximated by the…
New and refined bounds for expected maxima of fractional Brownian motion
Konstantin Borovkov, Yuliya Mishura, Alexander Novikov +1
For the fractional Brownian motion with the Hurst parameter value in (0,1/2), we derive new upper and lower bounds for the difference between the expectations of the maxi…
Bounds for expected maxima of Gaussian processes and their discrete approximations
Konstantin Borovkov, Yuliya Mishura, Alexander Novikov +1
The paper deals with the expected maxima of continuous Gaussian processes that are Hölder continuous in -norm and/or satisfy the opposite inequality for t…
Optimal stopping problems for a Brownian motion with a disorder on a finite interval
A. N. Shiryaev, M. V. Zhitlukhin
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a…