Reserve of Semi-Continuous Life Insurance Model under Random Interest Rate

2014 ◽  
Vol 998-999 ◽  
pp. 1626-1629
Author(s):  
Jing Wei ◽  
Shi Gang Ge
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Poisson Process ◽  
Uniform Distribution ◽  
Life Insurance ◽  
Stochastic Interest Rate ◽  
Reflected Brownian Motion ◽  
Stochastic Interest ◽  
The Common ◽  
Insurance Model

In this paper, it aims at an n-year term increasing life insurance model, considers the factual statements and the bursting out things’ influence on interest rate, establishes the model for stochastic interest rate by Reflected Brownian motion associating with Poisson process, and gives the common expression of semi-continuous reserve and the expression in the suppose of Uniform distribution of death.

scholarly journals Long-Term Returns in Stochastic Interest Rate Models: Applications

2000 ◽  
Vol 30 (1) ◽  
pp. 123-140 ◽  
Author(s):  
Griselda Deelstra
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Stochastic Interest Rate ◽  
Interest Rate Models ◽  
Monetary Policies ◽  
Brownian Motion With Drift ◽  
Convergence Results ◽  
Stochastic Interest ◽  
Explicit Formulae

AbstractWe extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral . For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.

European Option Pricing under Fractional Stochastic Interest Rate Model

2010 ◽  
Vol 171-172 ◽  
pp. 787-790
Author(s):  
Wen Li Huang ◽  
Gui Mei Liu ◽  
Sheng Hong Li ◽  
An Wang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Stochastic Interest Rate ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Pde Method ◽  
And Control

Under the assumption of stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with fractional stochastic interest rate. By choosing suitable Hurst index, we can calibrate the pricing model, so that the price can be used as the actual price of option and control the risk management

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