Results 1 
9 of
9
Multiscale stochastic volatility asymptotics
 SIAM J. MULTISCALE MODELING AND SIMULATION
, 2003
"... In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process that varies on several characteristic time scales. The classical BlackScholes formula gives the pri ..."
Abstract

Cited by 34 (15 self)
 Add to MetaCart
(Show Context)
In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process that varies on several characteristic time scales. The classical BlackScholes formula gives the price of call options when the underlying is a geometric Brownian motion with a constant volatility. The underlying might be the price of a stock or an index say and a constant volatility corresponds to a fixed standard deviation for the random fluctuations in the returns of the underlying. Modern market phenomena makes it important to analyze the situation when this volatility is not fixed but rather is heterogeneous and varies with time. In previous work, see for instance [5], we considered the situation when the volatility is fast mean reverting. Using a singular perturbation expansion we derived an approximation for option prices. We also provided a calibration method using observed option prices as represented by the socalled term structure of implied volatility. Our analysis of market data, however, shows the need for introducing also a slowly varying factor in the model for the stochastic volatility. The combination of regular and singular perturbations approach that we set forth in this paper deals with this case. The resulting approximation is still independent of the particular details of the volatility model and gives more flexibility in the parametrization of the
2004. Structured modeling of concurrent stochastic hybrid systems
 FORMATS LNCS 3253:309–24
"... Structured Modeling of Concurrent Stochastic Hybrid Systems We propose a modeling language for structured specification of interacting components with both hybrid and stochastic dynamics. The behavior of a stochastic hybrid agent is described using a hybrid automaton whose dynamics is specified by s ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
Structured Modeling of Concurrent Stochastic Hybrid Systems We propose a modeling language for structured specification of interacting components with both hybrid and stochastic dynamics. The behavior of a stochastic hybrid agent is described using a hybrid automaton whose dynamics is specified by stochastic differential equations and probabilistic jumps. Stochastic hybrid agents interact with other agents using shared variables. The operations of parallel composition, instantiation and hiding are defined to allow hierarchical descriptions of complex agents. We report on a stochastic extension of the modeling environment CHARON for hybrid systems, a simulation tool, and case studies using the tool.
Backward stochastic differential equations with respect to general filtrations and applications to insider finance
, 2009
"... ABSTRACT. In this article we obtain the ratio of risk investment and the optimal accumulated level of single premium endowment insurance in the case of dynamic investment strategies of life insurance company by BSDEs. It gives an illustration of traditional reserve valuation, and prudential rules. ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
ABSTRACT. In this article we obtain the ratio of risk investment and the optimal accumulated level of single premium endowment insurance in the case of dynamic investment strategies of life insurance company by BSDEs. It gives an illustration of traditional reserve valuation, and prudential rules.
Stability of an adaptive regulation for partially Known Nonlinear Stochastic Systems
 SIAM J. Control Optim
, 1999
"... ..."
(Show Context)
Two Deterministic Growth Models Related to DiffusionLimited Aggregation
, 1999
"... Growth models like DiffusionLimited Aggregation (DLA) have been actively studied in mathematics and physics the last twenty years. In this thesis we work on two deterministic models related to nonbranching conformal DLA, a model describing the growth, of a simply connected set of n >= 2 arcs in ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Growth models like DiffusionLimited Aggregation (DLA) have been actively studied in mathematics and physics the last twenty years. In this thesis we work on two deterministic models related to nonbranching conformal DLA, a model describing the growth, of a simply connected set of n >= 2 arcs in the plane with one common endpoint, along the external ray and in proportion to the harmonic measure of the tip of each arc. In its customary
Deterministic and Random Dynamical Systems: Theory and Numerics
, 2001
"... The theory of (random) dynamical systems is a framework for the analysis of large time behaviour of timeevolving systems (driven by noise). These notes contain an elementary introduction to the theory of both dynamical and random dynamical systems. The subject matter is made accessible by means ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The theory of (random) dynamical systems is a framework for the analysis of large time behaviour of timeevolving systems (driven by noise). These notes contain an elementary introduction to the theory of both dynamical and random dynamical systems. The subject matter is made accessible by means of very simple examples and highlights relationships between the deterministic and the random theories.
vorgelegt von
"... from uncovered interest rates parity towards the identification of exchange rates risk premia ..."
Abstract
 Add to MetaCart
from uncovered interest rates parity towards the identification of exchange rates risk premia
Contents
, 1998
"... 2. Enhanced di!usion with periodic or shortrange correlated velocity "elds 243 2.1. Homogenization theory for spatio ..."
Abstract
 Add to MetaCart
(Show Context)
2. Enhanced di!usion with periodic or shortrange correlated velocity "elds 243 2.1. Homogenization theory for spatio
Noisy quantum measurement of solidstate qubits
"... The quantum evolution of an individual solidstate qubit during the process of its continuous measurement can be described by the recently developed Bayesian formalism. In contrast to the conventional ensembleaveraged formalism, it takes into account the measurement record (in a way similar to the ..."
Abstract
 Add to MetaCart
(Show Context)
The quantum evolution of an individual solidstate qubit during the process of its continuous measurement can be described by the recently developed Bayesian formalism. In contrast to the conventional ensembleaveraged formalism, it takes into account the measurement record (in a way similar to the standard Bayesian analysis) and therefore is able to consider individual realizations of the measurement process. The formalism provides testable experimental predictions and can be used for the analysis of a quantum feedback control of solidstate qubits. The Bayesian formalism can be also applied to the continuous measurement of entangled qubits; in particular, it shows how to create a fully entangled pair of qubits without their direct interaction, just by measuring them with an equally coupled detector.