arXiv subjects

Erfan Salavati

Publications and source records attributed to Erfan Salavati.

11 recordsLinked to original sources

arXiv2025

Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence

Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during liquidity shocks. Using an Ito diffusion that may be connected with asset prices, we extend SPT to a continuous-time equity market with proportional, stochastic transaction costs. We derive closed-form lower bounds on cost-adjusted relative wealth for a large class of functionally generated portfolios; these bounds provide sufficient conditions for relative arbitrage to survive random costs. A limit-order-book cost proxy in conjunction with a Milstein scheme validates the theoretical order-of-magnitude estimates. Finally, we use intraday bid-ask spreads as a stand-in for cost volatility in a back-test of CRSP small-cap data (1994--2024). Despite experiencing larger declines during the 2008 and 2020 liquidity crises, diversity- and entropy-weighted portfolios continue to beat the value-weighted benchmark by 3.6 and 2.9 percentage points annually, respectively, after cost deduction.

q-fin.PM↗

arXiv2022

On a Class of Non-linear Differential Equations Arising from Branching Diffusions

A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using probabilistic ideas. We discuss non-negative solutions. We also generalize this idea to a class of non-linear parabolic differential equations which we call probabilistic parabolic equations.

math.PR↗

arXiv2022

Discretizations of Stochastic Evolution Equations in Variational Approach Driven by Jump-Diffusion

Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $σ$-finite intensity measure on a metric space. By using finite element methods and Galerkin approximations, some explicit and implicit discretizations for this equation are presented and their convergence is proved. Polynomial growth condition and linear growth condition are assumed on the drift operator, respectively for the implicit and explicit schemes.

math.PR↗

arXiv2019

An Extension of the Cardioid Distributions on Circle

A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property.

math.PR↗

arXiv2018

Local Coupling Property for Markov Processes with Applications to Lévy Processes

In this article, we define the new concept of local coupling property for Markov processes and study its relationship with distributional properties of the transition probability. In the special case of Lévy processes we show that this property is equivalent to the absolute continuity of the transition probability and also provide a sufficient condition for it in terms of the Lévy measure. Our result is stronger than existing results for absolute continuity of Lévy distributions.

math.PR↗

arXiv2016

Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$

Semilinear stochastic evolution equations with Lévy noise and monotone nonlinear drift are considered. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived. The main tool in our study is an Itô type inequality for the $p$th power of stochastic convolution integrals in Hilbert spaces.

math.PR↗

arXiv2016

A Sufficient Condition for Absolute Continuity of Infinitely Divisible Distributions

We consider infinitely divisible distributions with symmetric Lévy measure and study the absolute continuity of them with respect to the Lebesgue measure. We prove that if $η(r)=\int_{|x|\le r} x^2 ν(dx)$ where $ν$ is the Lévy measure, then $\int_0^1 \frac{r}{η(r)}dr <\infty$ is a sufficient condition for absolute continuity. As far as we know, our result is not implied by existing results about absolute continuity of infinitely divisible distributions.

math.PR↗

arXiv2015

A Maximal Inequality for $p$th Power of Stochastic Convolution Integrals

An inequality for the $p$th power of the norm of a stochastic convolution integral in a Hilbert space is proved. The inequality is stronger than analogues inequalities in the Literature in the sense that it is pathwise and not in expectation. An application of this inequality is provided for the semilinear stochastic evolution equations with Lévy noise and monotone nonlinear drift. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived.

math.PR↗

arXiv2014

Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed.

math.PR↗

arXiv2014

Continuous Dependence on Coefficients for Stochastic Evolution Equations with Multiplicative Lévy Noise and Monotone Nonlinearity

Semilinear stochastic evolution equations with multiplicative Lévy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients which as far as we know, has not been proved before. As corollaries of the continuity result, we derive sufficient conditions for asymptotic stability of the solutions, we show that Yosida approximations converge to the solution and we prove that solutions have Markov property. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed. The main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integrals.

math.PR↗

arXiv2013

Semilinear Stochastic Evolution Equations with Lévy Noise and Monotone Nonlinearity

Semilinear stochastic evolution equations with multiplicative Lévy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild solution is proved using an iterative method. The continuity of the solution with respect to initial conditions and coefficients is proved and a sufficient condition for exponential asymptotic stability of the solutions has been derived. The solutions are proved to have a Markov property. Examples on stochastic partial differential equations and stochastic delay equations are provided to demonstrate the theory developed. The main tool in our study is an Itô type inequality which gives a pathwise bound for the norm of stochastic convolution integrals.

math.PR↗