arXiv subjects

Sergey Lototsky

Publications and source records attributed to Sergey Lototsky.

6 recordsLinked to original sources

arXiv2025

Optimal Betting: Beyond the Long-Term Growth

While the Kelly portfolio has many desirable properties, including optimal long-term growth rate, the resulting investment strategy is rather aggressive. In this paper, we suggest a unified approach to the risk assessment of the Kelly criterion in both discrete and continuous time by introducing and analyzing the asymptotic variance that describes fluctuations of the portfolio growth, and use the results to propose two new measures for quantifying risk.

q-fin.RM↗

arXiv2021

Aggregate Cyber-Risk Management in the IoT Age: Cautionary Statistics for (Re)Insurers and Likes

In this paper, we provide (i) a rigorous general theory to elicit conditions on (tail-dependent) heavy-tailed cyber-risk distributions under which a risk management firm might find it (non)sustainable to provide aggregate cyber-risk coverage services for smart societies, and (ii)a real-data driven numerical study to validate claims made in theory assuming boundedly rational cyber-risk managers, alongside providing ideas to boost markets that aggregate dependent cyber-risks with heavy-tails.To the best of our knowledge, this is the only complete general theory till date on the feasibility of aggregate cyber-risk management.

cs.PF↗

arXiv2020

Gaussian Fields and Stochastic Heat Equations

The objective of the paper is to characterize the Gaussian free field as a stationary solution of the heat equation with additive space-time white noise. In the case of whole space, the investigation leads to other types of Gaussian fields, as well as interesting phenomena in dimensions one and two.

math.PR↗

arXiv2020

Kelly Criterion: From a Simple Random Walk to Lévy Processes

The original Kelly criterion provides a strategy to maximize the long-term growth of winnings in a sequence of simple Bernoulli bets with an edge, that is, when the expected return on each bet is positive. The objective of this work is to consider more general models of returns and the continuous time, or high frequency, limits of those models.

math.PR↗

arXiv2018

A String Model of Liquidity in Financial Markets

We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We prove that generically there is no arbitrage in the model when the driving noise is a stochastic string. Under the equivalent martingale measure, the clearing price is a martingale, and options can be priced under the no-arbitrage hypothesis. We consider several parameterized versions of the model, and show some advantages of specifying the demand curve as quantity as a function of price (as opposed to price as a function of quantity). We calibrate our model to real order book data, compute option prices by Monte Carlo simulation, and compare the results to observed data.

q-fin.MF↗

arXiv2008

Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter $H\geq 1/2$. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.

math.PR↗