Pricing and hedging of derivatives based on non-tradable underlyings (2007)
Ankirchner, Stefan, Imkeller, Peter, Reis, Goncalo Dos
This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable underlyings, but are correlated with tradable assets. We calculate...
Classical and Variational Differentiability of BSDEs with Quadratic Growth (2007)
Ankirchner, Stefan; Humboldt Uiversitaet Berlin; Ankirchn@mathematik.hu-berlin.de, Imkeller, Peter; Humboldt Uiversitaet Berlin; Imkeller@mathematik.hu-berlin.de, Dos Reis, Goncalo JN; Humboldt Uiversitaet Berlin; Gnreis@mathematik.hu-berlin.de
We consider Backward Stochastic Differential Equations (BSDEs) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition...
First exit times for L\'evy-driven diffusions with exponentially light jumps (2007)
Imkeller, Peter, Pavlyukevich, Ilya, Wetzel, Torsten
We consider a dynamical system described by the differential equation dY_t=-U'(Y_t)dt with a unique stable point at the origin. We perturb the system by L\'evy noise of intensity \e, to obtain the...
Optimal cross hedging for insurance derivatives (2007)
Ankirchner, Stefan, Imkeller, Peter, Popier, Alexandre
We consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. We assume that this process is correlated with a...
On measure solutions of backward stochastic differential equations (2007)
Ankirchner, Stefan, Imkeller, Peter, Popier, Alexandre
We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as...
Large deviations and a Kramers' type law for self-stabilizing diffusions (2007)
Herrmann, Samuel, Imkeller, Peter, Peithmann, Dierk
We investigate exit times from domains of attraction for the motion of a self-stabilized particle travelling in a geometric (potential type) landscape and perturbed by Brownian noise of small...
Global flows for stochastic differential equations without global Lipschitz conditions (2007)
Fang, Shizan, Imkeller, Peter, Zhang, Tusheng
We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field,...
Classical and Variational Differentiability of BSDEs with quadratic growth (2007)
Ankirchner, Stefan, Imkeller, Peter, Reis, Goncalo Dos
We consider Backward Stochastic Differential Equations (BSDE) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition...
Global flows for stochastic differential equations without global Lipschitz conditions (2007)
Fang, Shizan, Imkeller, Peter, Zhang, Tusheng
We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field,...
Global flows for stochastic differential equations without global Lipschitz conditions (2007)
Fang, Shizan, Imkeller, Peter, Zhang, Tusheng
We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field,...
Die Wiederentdeckung eines Mathematikers: Wolfgang Döblin (2007)
Imkeller, Peter, Roelly, Sylvie
"Considerons une particule mobile se mouvant aleatoirement sur la droite (ou sur un segment de droite). Supposons qu'il existe une probabilite F(x,y;s,t) bien definie pour que la particule se...
Die Wiederentdeckung eines Mathematikers: Wolfgang Döblin (2007)
Imkeller, Peter, Roelly, Sylvie
"Considerons une particule mobile se mouvant aleatoirement sur la droite (ou sur un segment de droite). Supposons qu'il existe une probabilite F(x,y;s,t) bien definie pour que la particule se...
Herrmann, Samuel, Imkeller, Peter, Peithmann, Dierk
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period T and a...
Large deviations and a Kramers' type law for self-stabilizing diffusions (2006)
Herrmann, Samuel, Imkeller, Peter, Peithmann, Dierk
We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small...
The Shannon information of filtrations and the additional logarithmic utility of insiders (2006)
Ankirchner, Stefan, Dereich, Steffen, Imkeller, Peter
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed...
Metastable Behaviour of Small Noise Levy-Driven Diffusions (2006)
Imkeller, Peter, Pavlyukevich, Ilya
We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small...
Utility maximization in incomplete markets (2005)
Hu, Ying, Imkeller, Peter, Muller, Matthias
We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we...
Utility maximization in incomplete markets (2005)
Hu, Ying, Imkeller, Peter, Müller, Matthias
We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors’ trading strategies we...
The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders (2005)
Ankirchner, Stefan, Imkeller, Peter, Dereich, Steffen
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed...
The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders (2005)
Ankirchner, Stefan, Imkeller, Peter, Dereich, Steffen
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed...
A two state model for noise-induced resonance in bistable systems with delay (2005)
Fischer, Markus, Imkeller, Peter
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what...
A two state model for noise-induced resonance in bistable systems with delay (2005)
Fischer, Markus, Imkeller, Peter
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what...
The exit problem for diffusions with time-periodic drift and stochastic resonance (2005)
Herrmann, Samuel, Imkeller, Peter
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not...
The Shannon information of filtrations and the additional logarithmic utility of insiders (2005)
Ankirchner, Stefan, Dereich, Steffen, Imkeller, Peter
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed...
The exit problem for diffusions with time-periodic drift and stochastic resonance (2005)
Herrmann, Samuel, Imkeller, Peter
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not...
Herrmann, Samuel, Imkeller, Peter, Peithmann, Dierk
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and...
Imkeller, Peter, Pavlyukevich, Ilya
We study the exit problem of solutions of the stochastic differential equation dX(t)=-U'(X(t))dt+epsilon dL(t) from bounded or unbounded intervals which contain the unique asymptotically stable...
Additional Utility of Insiders with Imperfect Dynamical Information (2003)
Corcuera, José Mª, Imkeller, Peter, Kohatsu-Higa, Arturo, Nualart, David
In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every...
Stochastic Resonance in Two-State Markov Chains (2003)
Imkeller, Peter, Pavlyukevich, Ilya
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying...
The Kramers Oscillator Revisited (2000)
In their 1993 paper [16], Schimansky-Geier and Herzel discovered numerically that the Kramers oscillator (which is identical with the Duffing oscillator forced by additive white noise) has a positive...
Rotation Numbers for Linear Stochastic Differential Equations (2000)
Let dx = P m i=0 A i x ffi dW i be a linear SDE in R d , generating the flow Phi t of linear isomorphisms. The multiplicative ergodic theorem asserts that every vector v 2 R d n f0g possesses a...
Peter Imkeller, Adam Hugh Monahan, Lionel P
. In this article we develop some mathematically rigorous ideas to explain the phenomenon of localisation of planetary waves in a stochastic background ow as presented in the physical companion...
An explicit description of the Lyapunov exponents of the noisy damped harmonic oscillator (2000)
Peter Imkeller, Christian Lederer
The Lyapunov exponents of the linearization x = x + _ x + t x of a noisy Dung-van der Pol oscillator are key quantities in the investigation of the stochastic Hopf bifurcation of this system....
Stochastic Confinement of Rossby Waves by Fluctuating Eastward Flows (2000)
Adam Hugh Monahan, Lionel P, Peter Imkeller
The effect of stochastic uctuations in the background zonal velocity field on the energy dispersion of stationary wave responses to meridionally localised forcing is considered, using the...
The Kramers Oscillator Revisited (2000)
In their 1993 paper [16], Schimansky-Geier and Herzel discovered numerically that the Kramers oscillator (which is identical with the Duffing oscillator forced by additive white noise) has a positive...
Energy Balance Models - viewed from Stochastic Dynamics (1999)
. In this article the bottom part in the hierarchy of climate models - energy balance models - are revisited by a mathematician working in stochastic dynamics. The review of mostly deterministic 0-...
Free Lunch and Arbitrage Possibilities in a Financial Market Model With an Insider (1999)
We consider financial market models based on Wiener space with two agents on di#erent information levels: a regular agent whose information is contained in the natural filtration of the Wiener...
On the Spatial Asymptotic Behavior of Stochastic Flows in Euclidean Space (1999)
Imkeller, Peter, Scheutzow, Michael
We study asymptotic growth rates of stochastic flows on $\mathbf{R}^d$ and their derivatives with respect to the spatial parameter under Lipschitz conditions on the local characteristics of the...
Rotation Numbers For Linear Stochastic Differential Equations (1999)
Arnold, Ludwig, Imkeller, Peter
Let $dx=\sum_{i=0}^{infty}$ be a linear SDE in $\mathbb{R}^d$, generating the flow $\Phi_t$ of linear isomorphisms. The multiplicative ergodic theorem asserts that every vector $v\in\mathbb{R}^d\{0}$...
Peter Imkeller, Bjorn Schmalfuss, Fb Angewandte Naturwissenschaften
We consider stochastic di#erential equations in d-dimensional Euclidean space driven by an m-dimensional Wiener process, determined by the drift vector field f 0 and the di#usion vector fields f 1 ,...
Bifurcation of One-Dimensional Stochastic Differential Equation (1998)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Bifurcation of One--Dimensional Stochastic Differential Equation (1998)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Unter Den Linden, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Bifurcation of One--Dimensional Stochastic Differential Equation (1998)
Hans Crauel, Fachbereich Mathematik, Sekr Ma, Peter Imkeller, Marcus Steinkamp
We consider families of random dynamical systems induced by parametrized one dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of...
Additional Logarithmic Utility of an Insider (1998)
J Amendinger, Peter Imkeller, Martin Schweizer
In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's...
Rotation Numbers for Linear Stochastic Differential Equations (1997)
Let dx = P m i=0 A i x ffi dW i be a linear SDE in R d , generating the flow Phi t of linear isomorphisms. The multiplicative ergodic theorem asserts that every vector v 2 R d n f0g possesses a...
. Fix two rectangles A, B in [0, 1] N . Then the size of the random set of double points of the N-parameter Brownian motion (W t ) t#[0,1] N in R d , i.e. the set of pairs (s, t), where s # A, t # B,...
The multiplicative ergodic theorem is valid under an integrability condition on the linearized flow with respect to an invariant measure. We investigate the case were the flow is generated by a...
Normal Forms for Stochastic Differential Equations (1997)
We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx t = P m j=0 f j (x t ) ffi dW j t and dx t = P m j=0 g j (x t ) ffi dW j t in R d with...
Let u(t; x); t 2 R; be an adapted process parametrized by a variable x in some metric space X , ¯(!; dx) a probability kernel on the product of the probability spaceOmega and the Borel sets of X ....
The Oseledets spaces of a random dynamical system generated by a linear stochastic di#erential equation are obtained as intersections of the corresponding nested invariant spaces of a forward and a...
Normal Forms for Stochastic Differential Equations (1997)
We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx t = P m j=0 f j (x t ) ffi dW j t and dx t = P m j=0 g j (x t ) ffi dW j t in R d with...
The multiplicative ergodic theorem is valid under an integrability condition on the linearized flow with respect to an invariant measure. We investigate the case were the flow is generated by a...
Two-parameter martingales and their quadratic variation / Peter Imkeller (1988)
Incluye bibliografía e índice
Additional Logarithmic Utility of an Insider (1970)
J Amendinger, Peter Imkeller, Martin Schweizer
In this paper, we consider a security market in which two investors on di#erent information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor's...
The Shannon Information of Filtrations and the Additional Logarithmic Utility of Insiders
Stefan Ankirchner, Steffen Dereich, Peter Imkeller
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed...
A two state model for noise-induced resonance in bistable systems with delay
Markus Fischer, Peter Imkeller
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what...
Additional Logarithmic Utility of an Insider
Amendinger, Jürgen, Imkeller, Peter, Schweizer, Martin
In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor’s...
Additional Logarithmic Utility of an Insider
Amendinger, Jürgen, Imkeller, Peter, Schweizer, Martin
In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor’s...
A Simple Model for Trading Climate Risk
Sébastien Chaumont, Peter Imkeller, Matthias Müller, Ulrich Horst
Klimaereignisse auf einer kurzen Zeitskala, wie die Anomalie der Oberflächentemperatur im Ozean, bekannt als El Niño, sind finanzielle Risikoquellen, die zu unvollständigen Märkten führen. Um so...
Additional Utility of Insiders with Imperfect Dynamical Information
José Mª Corcuera, Peter Imkeller, Arturo Kohatsu, David Nualart
In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every...
PARTIAL EQUILIBRIUM AND MARKET COMPLETION
YING HU, PETER IMKELLER, MATTHIAS MÃLLER
We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather...