Research Output
Articles
Publication Date: 2025
Sahand Communications In Mathematical Analysis (24233900)22(3)pp. 157-179
This paper presents an uncertainty framework, in which the volatility process exists within a random interval defined by bounds modeled by a Cox-Ingersoll-Ross (CIR) process. We analyzed the worst-case and best-case scenario prices of a simple contingent claim within this framework, demonstrating that it can be computed using prices from the parameterized Heston model. We also proved that if the payoff function is convex (concave), the worst-case and best-case scenario prices simplify to the price derived from the parametrized Heston model with specified parameters. Finally, we concluded with numerical examples to illustrate our findings. © 2025, University of Maragheh. All rights reserved.
Publication Date: 2023
Journal of Applied Probability (00219002)60(3)pp. 1096-1111
We study a sceptical rumour model on the non-negative integer line. The model starts with two spreaders at sites 0, 1 and sceptical ignorants at all other natural numbers. Then each sceptic transmits the rumour, independently, to the individuals within a random distance on its right after s/he receives the rumour from at least two different sources. We say that the process survives if the size of the set of vertices which heard the rumour in this fashion is infinite. We calculate the probability of survival exactly, and obtain some bounds for the tail distribution of the final range of the rumour among sceptics. We also prove that the rumour dies out among non-sceptics and sceptics, under the same condition. © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust.
Publication Date: 2020
Indian Journal of Pure and Applied Mathematics (00195588)51(4)pp. 1661-1671
We consider a model of the spread of rumour among sceptical individuals. Let X0, X1,… be a {0, 1}-valued Markov chain and ρ0, ρ1, … a sequence of i.i.d. ℕ valued random variables independent of the Markov chain. An individual located at site i ∈ ℕ*:= ℕ ∪ {0} spreads the rumour to the individuals located in the interval [i, i + ρi] provided (i) Xi = 1 and (ii) if s/he has received the rumour from at least two distinct sources j, k < i with Xj = Xk = 1. To start the process we place two individuals at locations −1 and −2, each of spread the rumour to a distance ρ−1 and ρ−2 respectively to the right of itself. Here ρ−1 and ρ−2 are i.i.d. copies of ρ0. This extends the work of Sajadi and Roy [7] who considered the case when X0, X1,… is a sequence of i.i.d. {0,1} valued random variables, i.e. the believers {i: Xi = 1} and the disbelievers {i: Xi = 0} are located in an i.i.d. fashion. Here we study the case when the the believers and the disbelievers are located in a Markovian fashion. © 2020, Indian National Science Academy.
Publication Date: 2019
Bulletin Of The Iranian Mathematical Society (10186301)45(1)pp. 283-301
We consider a Dynkin game where the seller possesses additional information compared to the buyer. The additional information is described by a random variable taking finitely many values. We show that the game possesses a value and we provide a necessary and sufficient condition for the existence of a Nash equilibrium. Results are illustrated with an explicit example. © 2018, Iranian Mathematical Society.
