Results 1 
9 of
9
Convergence of discretized stochastic (interest rate) processes with stochastic drift term
 Appl. Stochastic Models Data Anal
, 1998
"... For applications in finance, we study the stochastic differential equation dXs = (2βXs+δs)ds+g(Xs)dBs with β a negative real number, g a continuous function vanishing at zero which satisfies a Hölder condition and δ a measurable and adapted stochastic process such that ∫ t 0 δudu < ∞ a.e. for all ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
For applications in finance, we study the stochastic differential equation dXs = (2βXs+δs)ds+g(Xs)dBs with β a negative real number, g a continuous function vanishing at zero which satisfies a Hölder condition and δ a measurable and adapted stochastic process such that ∫ t 0 δudu < ∞ a.e. for all t ∈ IR + and which may have a random correlation with the process X itself. In this paper, we concentrate on the Euler discretization scheme for such processes and we study the convergence in L1supnorm and in H1norm towards the solution of the stochastic differential equation with stochastic drift term. We also check the order of strong convergence. KEY WORDS Stochastic differential equation stochastic drift term Hölder condition Euler discretization scheme strong convergence 1.1. Aim of the present study 1.
Strong solutions of a class of SDEs with jumps
, 2008
"... We study a class of stochastic integral equations with jumps under nonLipschitz conditions. We use the method of Euler approximations to obtain the existence of the solution and give some sufficient conditions for the strong uniqueness. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We study a class of stochastic integral equations with jumps under nonLipschitz conditions. We use the method of Euler approximations to obtain the existence of the solution and give some sufficient conditions for the strong uniqueness.
Ergodicity of scalar stochastic differential equations with Hoelder continuous coeffcients Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients
"... ..."
(Show Context)
Consistent fitting of onefactor models to interest rate data
, 2000
"... We describe a full maximumlikelihood fitting method of the popular singlefactor Vasicek and Cox–Ingersoll–Ross models and carry this out for termstructure data from the UK and US. This method contrasts with the usual practice of performing a daybyday fit. We also compare the results with some m ..."
Abstract
 Add to MetaCart
We describe a full maximumlikelihood fitting method of the popular singlefactor Vasicek and Cox–Ingersoll–Ross models and carry this out for termstructure data from the UK and US. This method contrasts with the usual practice of performing a daybyday fit. We also compare the results with some more crude econometric analyses on the same data sets. © 2000 Elsevier Science B.V. All rights reserved.
LongTerm Behaviors of Stochastic Interest Rate Models with Jumps and Memory
"... ar ..."
(Show Context)
DIFFUSION APPROXIMATION OF RECURRENT SCHEMES FOR FINANCIAL MARKETS, WITH APPLICATION TO THE ORNSTEINUHLENBECK PROCESS
"... Abstract. We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discretetime models of a financial market to the continuoustime diffusion model. These results generalize a classical sch ..."
Abstract
 Add to MetaCart
Abstract. We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discretetime models of a financial market to the continuoustime diffusion model. These results generalize a classical scheme of the weak convergence for discretetime markets to the BlackScholes model. We give an explicit and direct method of approximation by a recurrent scheme. As an example, an OrnsteinUhlenbeck process is considered as a limit model.
SUMMARY
"... For applications in finance, we study the stochastic differential equation dXs = (2βXs + δs)ds+ g(Xs)dBs with β a negative real number, g a continuous function vanishing at zero which satisfies a Hölder condition and δ a measurable and adapted stochastic process such that ∫ t 0 δudu < ∞ a.e. fo ..."
Abstract
 Add to MetaCart
For applications in finance, we study the stochastic differential equation dXs = (2βXs + δs)ds+ g(Xs)dBs with β a negative real number, g a continuous function vanishing at zero which satisfies a Hölder condition and δ a measurable and adapted stochastic process such that ∫ t 0 δudu < ∞ a.e. for all t ∈ IR+ and which may have a random correlation with the process X itself. In this paper, we concentrate on the Euler discretization scheme for such processes and we study the convergence in L1supnorm and in H1norm towards the solution of the stochastic differential equation with stochastic drift term. We also check the order of strong convergence. KEY WORDS Stochastic differential equation stochastic drift term Hölder condition Euler discretization scheme strong convergence 1.
1 LONGTERM RETURNS IN STOCHASTIC INTEREST RATE MODELS: DIFFERENT CONVERGENCE RESULTS.
"... Abstract: In this paper, we focus on different convergence results of the longterm return 1 t rudu0 t ∫ , where the short interest rate r follows an extension of the Cox, Ingersoll and Ross1 model. Using the theory of Bessel processes, we proved the convergence almost everywhere of 1 t ..."
Abstract
 Add to MetaCart
Abstract: In this paper, we focus on different convergence results of the longterm return 1 t rudu0 t ∫ , where the short interest rate r follows an extension of the Cox, Ingersoll and Ross1 model. Using the theory of Bessel processes, we proved the convergence almost everywhere of 1 t