scholarly journals A remark on optimal variance stopping problems

2015 ◽  
Vol 52 (4) ◽  
pp. 1187-1194 ◽  
Author(s):  
Bruno Buonaguidi
Keyword(s):  
Stochastic Process ◽  
Diffusion Process ◽  
Interest Rates ◽  
Solution Method ◽  
Stopping Time ◽  
Initial Problem

In an optimal variance stopping problem the goal is to determine the stopping time at which the variance of a sequentially observed stochastic process is maximized. A solution method for such a problem has been recently provided by Pedersen (2011). Using the methodology developed by Pedersen and Peskir (2012), our aim is to show that the solution to the initial problem can be equivalently obtained by constraining the variance stopping problem to the expected size of the stopped process and then by maximizing the solution to the latter problem over all the admissible constraints. An application to a diffusion process used for modeling the dynamics of interest rates illustrates the proposed technique.

scholarly journals A remark on optimal variance stopping problems

2015 ◽  
Vol 52 (04) ◽  
pp. 1187-1194 ◽  
Author(s):  
Bruno Buonaguidi
Keyword(s):  
Stochastic Process ◽  
Diffusion Process ◽  
Interest Rates ◽  
Solution Method ◽  
Stopping Time ◽  
Initial Problem

In an optimal variance stopping problem the goal is to determine the stopping time at which the variance of a sequentially observed stochastic process is maximized. A solution method for such a problem has been recently provided by Pedersen (2011). Using the methodology developed by Pedersen and Peskir (2012), our aim is to show that the solution to the initial problem can be equivalently obtained by constraining the variance stopping problem to the expected size of the stopped process and then by maximizing the solution to the latter problem over all the admissible constraints. An application to a diffusion process used for modeling the dynamics of interest rates illustrates the proposed technique.

scholarly journals PERHITUNGAN PREMI ASURANSI JOINT LIFE DENGAN MODEL VASICEK DAN CIR

2019 ◽  
Vol 8 (3) ◽  
pp. 246
Author(s):  
I MADE WAHYU WIGUNA ◽  
KETUT JAYANEGARA ◽  
I NYOMAN WIDANA
Keyword(s):  
Stochastic Process ◽  
Interest Rates ◽  
Life Insurance ◽  
Insurance Premium ◽  
Insurance Contract ◽  
Insurance Company ◽  
Vasicek Model ◽  
Cir Model ◽  
Premium Payment ◽  
Premium Price

Premium is a sum of money that must be paid by insurance participants to insurance company, based on  insurance contract. Premium payment are affected by interest rates. The interest rates change according to stochastic process. The purpose of this work is to calculate the price of joint life insurance premiums with Vasicek and CIR models. The price of a joint life insurance premium with Vasicek and CIR models, at the age of the insured 35 and 30 years has increased until the last year of the contract. The price of a joint life insurance premium with Vasicek model is more expensive than the premium price using CIR model.

About the # Function

1976 ◽  
Vol 19 (4) ◽  
pp. 455-460
Author(s):  
G. T. Klincsek
Keyword(s):  
Stochastic Process ◽  
Stopping Time ◽  
Decreasing Rearrangement ◽  
Image Position

AbstractThe use of decreasing rearrangement formulas, and particularly that of the weak N inequality, is illustrated by deriving from Eτ |f-f(τ -)|≤Eτu (where ft is some stochastic process and τ arbitrary stopping time) the estimate ||f||≤Const||u|| in the class of structureless norms with finite dual Hardy bound.The basic estimate is

Optimal stopping of a risk process: model with interest rates

2002 ◽  
Vol 39 (2) ◽  
pp. 261-270 ◽  
Author(s):  
Bogdan Krzysztof Muciek
Keyword(s):  
Interest Rates ◽  
Optimal Stopping ◽  
Process Model ◽  
Stopping Time ◽  
Risk Process ◽  
Risk Theory ◽  
Dynamic Programming Method ◽  
Insurance Company ◽  
Initial Capital ◽  
The Times

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a ≥ 0, receives premiums and pays out claims that occur according to a renewal process {N(t), t ≥ 0}. The times between consecutive claims are i.i.d. The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested at interest rate α ∊ [0,1], claims increase at rate β ∊ [0,1]. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time.

Optimal stopping of a risk process: model with interest rates

2002 ◽  
Vol 39 (02) ◽  
pp. 261-270 ◽  
Author(s):  
Bogdan Krzysztof Muciek
Keyword(s):  
Interest Rates ◽  
Optimal Stopping ◽  
Process Model ◽  
Stopping Time ◽  
Risk Process ◽  
Risk Theory ◽  
Dynamic Programming Method ◽  
Insurance Company ◽  
Initial Capital ◽  
The Times

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a ≥ 0, receives premiums and pays out claims that occur according to a renewal process {N(t), t ≥ 0}. The times between consecutive claims are i.i.d. The sequence of successive claims is a sequence of i.i.d. random variables. The capital of the company is invested at interest rate α ∊ [0,1], claims increase at rate β ∊ [0,1]. The aim is to find the stopping time that maximizes the capital of the company. A dynamic programming method is used to find the optimal stopping time and to specify the expected capital at that time.

Research on Stock Analysis Based on Stochastic Process

2012 ◽  
Vol 433-440 ◽  
pp. 5967-5974
Author(s):  
Pei Ze Li
Keyword(s):  
Stochastic Process ◽  
Stock Prices ◽  
Stock Price ◽  
Statistical Physics ◽  
Stopping Time ◽  
Mathematical Finance ◽  
Market Condition ◽  
Price Process ◽  
Physics Model ◽  
Statistical Physics Model

In stock market, the stock prices directly reflects market condition, therefore, the research on stock price process is one of the research contents of mathematical finance. In this paper by using the election model of statistical physics model to study the stock price fluctuation . This paper first applying stochastic process theory to establish election model, then the election model and stopping time theory are applied to establish stock profit process, we get the stock price process.

scholarly journals EXTENSION OF VASICEK MODEL TO THE MODELLING OF INTEREST RATE

2020 ◽  
Vol 4 (2) ◽  
pp. 151-155
Author(s):  
Adaobi Udoye ◽  
Lukman Akinola ◽  
Eka Ogbaji
Keyword(s):  
Stochastic Process ◽  
Interest Rate ◽  
Interest Rates ◽  
Regression Method ◽  
Least Square ◽  
Interesting Aspect ◽  
Vasicek Model ◽  
Least Square Regression ◽  
Ito's Lemma ◽  
Random Times

Interest rate modelling is an interesting aspect of stochastic processes. It has been observed that interest rates fluctuates at random times, hence the need for its modelling as a stochastic process. In this paper, we apply the existing Vasicek model, Itô’s lemma and least-square regression method in the modelling and providing dynamics for a given interest rate.

scholarly journals The Dynamic Spread of the Forward CDS with General Random Loss

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Kun Tian ◽  
Dewen Xiong ◽  
Zhongxing Ye
Keyword(s):  
Interest Rates ◽  
Stopping Time ◽  
Random Measure ◽  
Random Variable ◽  
Conditional Density ◽  
Default Time ◽  
Defaultable Bond ◽  
Term Structures ◽  
Stochastic Interest ◽  
Random Loss

We assume that the filtrationFis generated by ad-dimensional Brownian motionW=(W1,…,Wd)′as well as an integer-valued random measureμ(du,dy). The random variableτ~is the default time andLis the default loss. LetG={Gt;t≥0}be the progressive enlargement ofFby(τ~,L); that is,Gis the smallest filtration includingFsuch thatτ~is aG-stopping time andLisGτ~-measurable. We mainly consider the forward CDS with loss in the framework of stochastic interest rates whose term structures are modeled by the Heath-Jarrow-Morton approach with jumps under the general conditional density hypothesis. We describe the dynamics of the defaultable bond inGand the forward CDS with random loss explicitly by the BSDEs method.

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