scholarly journals Adaptive nonparametric drift estimation of an integrated jump diffusion process

2018 ◽  
Vol 22 ◽  
pp. 236-260 ◽  
Author(s):  
Benedikt Funke ◽  
Émeline Schmisser
Keyword(s):  
Diffusion Process ◽  
High Frequency ◽  
Jump Diffusion ◽  
High Frequency Data ◽  
Compact Set ◽  
Penalized Least Squares ◽  
Adaptive Estimator ◽  
Drift Estimation ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the drift on a compact set based on a high-frequency data sample. Instead of observing the jump diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process Xt := ∫0t Vsds Based on the available observations of Xt, we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L2-risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.

NONPARAMETRIC ESTIMATION FOR SECOND-ORDER JUMP-DIFFUSION MODEL IN HIGH FREQUENCY DATA

2017 ◽  
Vol 65 (04) ◽  
pp. 1033-1063 ◽  
Author(s):  
YUPING SONG
Keyword(s):  
High Frequency ◽  
Jump Diffusion ◽  
Small Sample ◽  
Second Order ◽  
Stock Index ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Frequency Data ◽  
Sample Paths ◽  
Jump Diffusion Model

We provide the nonparametric estimators of the infinitesimal coefficients of the second-order continuous-time models with discontinuous sample paths of jump-diffusion models. Under the mild conditions, we obtain the weak consistency and the asymptotic normality of the estimators. A Monte Carlo experiment demonstrates the better small-sample performance of these estimators. In addition, the estimators are illustrated empirically through stock index of Shanghai Stock Exchange in high frequency data.

OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS

2021 ◽  
pp. 1-25
Author(s):  
CAIBIN ZHANG ◽  
ZHIBIN LIANG ◽  
KAM CHUEN YUEN
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

Abstract We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Optimal portfolio and consumption for a Markovian regime-switching jump-diffusion process

2021 ◽  
Vol 63 ◽  
pp. 308-332
Author(s):  
Caibin Zhang ◽  
Zhibin Liang ◽  
Kam Chuen Yuen
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.   doi:10.1017/S1446181121000122

Productivity Assessment Based on Jump Diffusion Model Considering the Effort Management for OSS Project

2019 ◽  
Vol 26 (05) ◽  
pp. 1950022 ◽  
Author(s):  
Yoshinobu Tamura ◽  
Hironobu Sone ◽  
Shigeru Yamada
Keyword(s):  
Project Management ◽  
Diffusion Process ◽  
Process Model ◽  
Jump Diffusion ◽  
Equation Model ◽  
Operation Performance ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model ◽  
Productivity Assessment

Various open source software (OSS) projects are in action around the world. Many OSS are developed and maintained under these OSS projects. Considering the characteristics of OSS, the operation performance of OSS development will take an irregular fluctuation in the long term of operation, because several developers and many users are closely related to the maintenance of OSS. This paper focuses on the irregular fluctuation of the operation performance of OSS. We apply the jump diffusion process model to the noisy cases in the operation of OSS. In particular, the maintenance effort is estimated by the stochastic differential equation model in terms of OSS project management. Moreover, we discuss the method of maintenance effort management based on jump diffusion process model considering the irregular fluctuation of performance for OSS projects. In particular, we propose the method of productivity assessment based on the proposed jump diffusion models. Thereby, it is helpful for the OSS development managers to understand the effort status of OSS from the standpoint of OSS project management. Also, we analyze actual data to show numerical examples of the proposed method considering the characteristics of OSS projects.

scholarly journals Jump Adapted Scheme Of a Non Mark Dependent Jump Diffusion Process with Application to the Merton Jump Diffusion Model

2017 ◽  
Vol 5 (4) ◽  
pp. 80
Author(s):  
Renaud Fadonougbo ◽  
George O. Orwa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Diffusion Process ◽  
Strong Convergence ◽  
General Result ◽  
Jump Diffusion ◽  
Discretization Scheme ◽  
Complete Proof ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

This paper provides a complete proof of the strong convergence of the Jump adapted discretization Scheme in the univariate and mark independent jump diffusion process case. We put in detail and clearly a known and general result for mark dependent jump diffusion process. A Monte-Carlo simulation is used as well to show numerical evidence.

scholarly journals Pricing Warrant Bonds with Credit Risk under a Jump Diffusion Process

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiaonan Su ◽  
Wei Wang ◽  
Wensheng Wang
Keyword(s):  
Numerical Analysis ◽  
Diffusion Process ◽  
Default Risk ◽  
Stock Price ◽  
Jump Diffusion ◽  
Pricing Model ◽  
Default Intensity ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model ◽  
The Interest Rate

This article investigates the pricing of the warrant bonds with default risk under a jump diffusion process. We assume that the stock price follows a jump diffusion model while the interest rate and the default intensity have the feature of mean reversion. By the risk neutral pricing theorem, we obtain an explicit pricing formula of the warrant bond. Furthermore, numerical analysis is provided to illustrate the sensitivities of the proposed pricing model.

Sign in / Sign up

Export Citation Format

Share Document