arXiv subjects

Qiang Yao

Publications and source records attributed to Qiang Yao.

22 records · Page 2Linked to original sources

arXiv2015

Weak Convergence of Equity Derivatives Pricing with Default Risk

This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we deduce the Arrow--Debreu state prices and the explicit pricing result in discrete time after embedding default risk in the pricing model. We prove that the discrete--time defaultable equity derivatives pricing has convergence stability, and it converges weakly to the continuous--time pricing results.

math.PR↗

arXiv2012

Metastable Densities for Contact Processes on Power Law Random Graphs

We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett, who showed that for arbitrarily small infection parameter $λ$, the survival time of the process is larger than a stretched exponential function of the number of vertices, $n$. We obtain sharp bounds for the typical density of infected sites in the graph, as $λ$ is kept fixed and $n$ tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.

math.PR↗

arXiv2012

The Complete Convergence Theorem Holds for Contact Processes in a Random Environment on $Z^d\times Z^+$

In this article, we consider the basic contact process in a static random environment on the half space $Z^d\times Z^+$ where the recovery rates are constants and the infection rates are independent and identically distributed random variables. We show that, for almost every environment, the complete convergence theorem holds. This is a generalization of the known result for the classical contact process in the half space case.

math.PR↗

arXiv2012

Exponential extinction time of the contact process on finite graphs

We study the extinction time $\uptau$ of the contact process on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on $\Z$, then, uniformly over all trees of degree bounded by a given number, the expectation of $\uptau$ grows exponentially with the number of vertices. Additionally, for any sequence of growing trees of bounded degree, $\uptau$ divided by its expectation converges in distribution to the unitary exponential distribution. These also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree. Using these results, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett \cite{CD}, we show that, for any infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices.

math.PR↗