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- Peter Jagers, Fima C. Klebaner
- Journal of theoretical biology
- 2003

Even though the efficiency of the polymerase chain reaction (PCR) reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency). Recently, Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enzyme kinetics. This results in the… (More)

- Peter Jagers, Fima C. Klebaner, Serik Sagitov
- Proceedings of the National Academy of Sciences…
- 2007

Populations can die out in many ways. We investigate one basic form of extinction, stable or intrinsic extinction, caused by individuals on the average not being able to replace themselves through reproduction. The archetypical such population is a subcritical branching process, i.e., a population of independent, asexually reproducing individuals, for which… (More)

The purpose of this note is to give a PDE satisfied by a call option when the price process is a semimartingale. The main result generalizes the PDE in the case when the stock price is a diffusion. Its proof uses Meyer-Tanaka and occupation density formulae. Presented approach also gives a new insight into the classical Black-Scholes formula. Rigorous… (More)

We consider a Markov chain X n obtained by adding small noise to a discrete time dynamical system and study the chain's quasi-stationary distribution (qsd). The dynamics is given by iterating a function f : I ! I for some interval I when f has nitely many xed points, some stable and some unstable. We show that under some conditions the quasi-stationary… (More)

Using a stochastic implied volatility method we show how to introduce smiles and skews into the BGM interest rate model.

- Yu Tian, Zili Zhu, Fima C. Klebaner, Kais Hamza
- 2010 IEEE Workshop on High Performance…
- 2010

In this paper, we will present our research on the acceleration for option pricing using Monte Carlo techniques on the GPU. We first introduce some basic ideas of GPU programming and then the stochastic volatility SABR model. Under the SABR model, we discuss option pricing with Monte Carlo techniques. In particular, we focus on European option pricing using… (More)

We construct a family of martingales with Gaussian marginal distributions. We give a weak construction as Markov, inhomogeneous in time processes, and compute their infinitesimal generators. We give the predictable quadratic variation and show that the paths are not continuous. The construction uses distributions Gσ having a logconvolution semigroup… (More)

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time… (More)

- Konstantin Borovkov, Fima C. Klebaner, Eleanor Virag
- Finance and Stochastics
- 2003

The following problem has been recently addressed in [5], [6]. The authors considered a continuous time subcritical branching process Z = (Zt)t≥0, starting from the initial population of size Z0 = x . As is well known, Zt gets extinct at the random time T = inf{t ≥ 0 : Zt = 0}, and T < ∞ with probability one. What can be said about ZT/2, i.e. the population… (More)