scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

scholarly journals The 𝒮-Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhi Wang ◽  
Litan Yan
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Stochastic Integral ◽  
Noise Analysis ◽  
Explicit Solutions ◽  
Pettis Integral ◽  
White Noise Analysis ◽  
Subfractional Brownian Motion

Let SH be a subfractional Brownian motion with index 0<H<1. Based on the 𝒮-transform in white noise analysis we study the stochastic integral with respect to SH, and we also prove a Girsanov theorem and derive an Itô formula. As an application we study the solutions of backward stochastic differential equations driven by SH of the form -dYt=f(t,Yt,Zt)dt-ZtdStH, t∈[0,T],YT=ξ, where the stochastic integral used in the above equation is Pettis integral. We obtain the explicit solutions of this class of equations under suitable assumptions.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

Stability of stochastic differential equations driven by multifractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oussama El Barrimi ◽  
Youssef Ouknine
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stationary Process ◽  
Strong Stability ◽  
Pathwise Uniqueness ◽  
Uniqueness Property ◽  
Selection Theorem ◽  
Multifractional Brownian Motion ◽  
Stability Results

Abstract Our aim in this paper is to establish some strong stability results for solutions of stochastic differential equations driven by a Riemann–Liouville multifractional Brownian motion. The latter is defined as a Gaussian non-stationary process with a Hurst parameter as a function of time. The results are obtained assuming that the pathwise uniqueness property holds and using Skorokhod’s selection theorem.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

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