Damien Lamberton
Research Subjects
Damien Lamberton has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- El Hadj Aly Dia
Université Paris-Est
2 shared publications - Gilles Pagès
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France
2 shared publications - Mohammed Mikou
Ecole Internationale des Sciences du Traitement de l'Information
2 shared publications - Mihail Zervos
Department of Mathematics London School of Economics Houghton Street WC2A 2AE London UK
1 shared publication - Mohammed Adam Mikou
École Internationale des Sciences du Traitement de l’Information
1 shared publication - Mohammed Mikou
Université Paris-Est
1 shared publication
Latest Publications
- 5 September 2012
- Published by Springer Nature in Finance and Stochastics
- Vol. 17 (2) , 355-394
Exercise boundary of the American put near maturity in an exponential Lévy model
- 5 September 2012
- Published by Springer Nature in Finance and Stochastics
- Vol. 17 (2) , 355-394
Exercise boundary of the American put near maturity in an exponential Lévy model
- Open Access
On the Optimal Stopping of a One-dimensional Diffusion
We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function $r$ that is uniformly bounded away from 0, we establish a new analytic representation of the $r$-potential of a continuous additive functional of the diffusion. We also characterize the value function of an optimal stopping problem with general reward function as the unique solution of a variational inequality (in the sense of distributions) with appropriate growth or boundary conditions. Furthermore, we establish several other characterisations of the solution to the optimal stopping problem, including a generalisation of the so-called "principle of smooth fit".Open AccessOn the Optimal Stopping of a One-dimensional Diffusion
We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function $r$ that is uniformly bounded away from 0, we establish a new analytic representation of the $r$-potential of a continuous additive functional of the diffusion. We also characterize the value function of an optimal stopping problem with general reward function as the unique solution of a variational inequality (in the sense of distributions) with appropriate growth or boundary conditions. Furthermore, we establish several other characterisations of the solution to the optimal stopping problem, including a generalisation of the so-called "principle of smooth fit". - 1 March 2012
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 49 (01) , 137-149
The Smooth-Fit Property in an Exponential Lévy Model
We study the smooth-fit property of the American put price with finite maturity in an exponential Lévy model when the underlying stock pays dividends at a continuous rate. As in the perpetual case, a regularity property is sufficient for smooth fit to occur. We also derive conditions on the Lévy measure under which smooth fit fails.
- 1 March 2012
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 49 (01) , 137-149
The Smooth-Fit Property in an Exponential Lévy Model
We study the smooth-fit property of the American put price with finite maturity in an exponential Lévy model when the underlying stock pays dividends at a continuous rate. As in the perpetual case, a regularity property is sufficient for smooth fit to occur. We also derive conditions on the Lévy measure under which smooth fit fails.
- Open Access
Exercise Boundary of the American Put Near Maturity in an Exponential Lévy Model
We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying L\'evy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that, when the negative part of the L\'evy measure exhibits an $\alpha$-stable density near the origin, with $1<\alpha<2$, the convergence rate is ruled by $\theta^{1/\alpha}|\ln \theta|^{1-\frac{1}{\alpha}}$, where $\theta$ is time until maturity.Open AccessExercise Boundary of the American Put Near Maturity in an Exponential Lévy Model
We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying L\'evy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that, when the negative part of the L\'evy measure exhibits an $\alpha$-stable density near the origin, with $1<\alpha<2$, the convergence rate is ruled by $\theta^{1/\alpha}|\ln \theta|^{1-\frac{1}{\alpha}}$, where $\theta$ is time until maturity. - Open Access
Continuity correction for barrier options in jump-diffusion models
The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with respect to the jump times and to the values of the underlying at the jump times and rely on the connection between the maximum of the Brownian motion and Bessel processes.
Open AccessContinuity correction for barrier options in jump-diffusion models
The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with respect to the jump times and to the values of the underlying at the jump times and rely on the connection between the maximum of the Brownian motion and Bessel processes.
- Open Access
Connecting discrete and continuous lookback or hindsight options in exponential Lévy models
Motivated by the pricing of lookback options in exponential L\'evy models, we study the difference between the continuous and discrete supremum of L\'evy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential L\'evy models.
Open AccessConnecting discrete and continuous lookback or hindsight options in exponential Lévy models
Motivated by the pricing of lookback options in exponential L\'evy models, we study the difference between the continuous and discrete supremum of L\'evy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential L\'evy models.
- 18 September 2008
- Published by Springer Nature in Finance and Stochastics
- Vol. 12 (4) , 561-581
The critical price for the American put in an exponential Lévy model
- 18 September 2008
- Published by Springer Nature in Finance and Stochastics
- Vol. 12 (4) , 561-581
The critical price for the American put in an exponential Lévy model
- Open Access
A penalized bandit algorithm
We study a two armed-bandit algorithm with penalty. We show the convergence of the algorithm and establish the rate of convergence. For some choices of the parameters, we obtain a central limit theorem in which the limit distribution is characterized as the unique stationary distribution of a discontinuous Markov process.
Open AccessA penalized bandit algorithm
We study a two armed-bandit algorithm with penalty. We show the convergence of the algorithm and establish the rate of convergence. For some choices of the parameters, we obtain a central limit theorem in which the limit distribution is characterized as the unique stationary distribution of a discontinuous Markov process.
- Open Access
How fast is the bandit?
In this paper we investigate the rate of convergence of the so-called two-armed bandit algorithm in a financial context of asset allocation. The behaviour of the algorithm turns out to be highly non-standard: no CLT whatever the time scale, possible existence of two rate regimes.
Open AccessHow fast is the bandit?
In this paper we investigate the rate of convergence of the so-called two-armed bandit algorithm in a financial context of asset allocation. The behaviour of the algorithm turns out to be highly non-standard: no CLT whatever the time scale, possible existence of two rate regimes.