scholarly journals Stochastic Comparison of Discounted Rewards

2011 ◽  
Vol 48 (1) ◽  
pp. 293-294 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Stochastic Process ◽  
Stopping Time ◽  
Stochastic Comparison ◽  
Convex Ordering ◽  
Total Reward ◽  
Discounted Rewards

It is well know that the expected exponentially discounted total reward for a stochastic process can also be defined as the expected total undiscounted reward earned before an independent exponential stopping time (let us call this the stopped reward). Feinberg and Fei (2009) recently showed that the variance of the discounted reward is smaller than the variance of the stopped reward. We strengthen this result to show that the discounted reward is smaller than the stopped reward in the convex ordering sense.

scholarly journals Stochastic Comparison of Discounted Rewards

2011 ◽  
Vol 48 (01) ◽  
pp. 293-294
Author(s):  
Rhonda Righter
Keyword(s):  
Stochastic Process ◽  
Stopping Time ◽  
Stochastic Comparison ◽  
Convex Ordering ◽  
Total Reward ◽  
Discounted Rewards

It is well know that the expected exponentially discounted total reward for a stochastic process can also be defined as the expected total undiscounted reward earned before an independent exponential stopping time (let us call this the stopped reward). Feinberg and Fei (2009) recently showed that the variance of the discounted reward is smaller than the variance of the stopped reward. We strengthen this result to show that the discounted reward is smaller than the stopped reward in the convex ordering sense.

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

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 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.

Enlargement of σ-Algebras and Compactness of Time Changes

1977 ◽  
Vol 29 (5) ◽  
pp. 1055-1065 ◽  
Author(s):  
J. R. Baxter ◽  
R. V. Chacon
Keyword(s):  
Stochastic Process ◽  
Probability Space ◽  
Stopping Time ◽  
Stopping Times ◽  
Complete Theory ◽  
Time Changes ◽  
Convergent Sequences

Given a stochastic process adapted to an increasing family of right-continuous σ-algebras, it is often useful for many purposes to enlarge the a-algebras. In the present paper we shall consider enlargements which involve embedding the process in a larger probability space. The first question investigated is what kinds of enlargements it might be useful to consider. To study stopping times, the least requirement needed to have a complete theory is that convergent sequences of stopping times converge to a function which is also a stopping time, and for this it is necessary to make the enlargement right continuous.

scholarly journals An Inequality for Variances of the Discounted Rewards

2009 ◽  
Vol 46 (04) ◽  
pp. 1209-1212 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Jun Fei
Keyword(s):  
Exponential Distribution ◽  
Stopping Time ◽  
Discounted Rewards ◽  
Multiplicative Coefficient

We consider the following two definitions of discounting: (i) multiplicative coefficient in front of the rewards, and (ii) probability that the process has not been stopped if the stopping time has an exponential distribution independent of the process. It is well known that the expected total discounted rewards corresponding to these definitions are the same. In this note we show that, the variance of the total discounted rewards is smaller for the first definition than for the second definition.

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 An Inequality for Variances of the Discounted Rewards

2009 ◽  
Vol 46 (4) ◽  
pp. 1209-1212 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Jun Fei
Keyword(s):  
Exponential Distribution ◽  
Stopping Time ◽  
Discounted Rewards ◽  
Multiplicative Coefficient

We consider the following two definitions of discounting: (i) multiplicative coefficient in front of the rewards, and (ii) probability that the process has not been stopped if the stopping time has an exponential distribution independent of the process. It is well known that the expected total discounted rewards corresponding to these definitions are the same. In this note we show that, the variance of the total discounted rewards is smaller for the first definition than for the second definition.

scholarly journals $L^{p}-$Variational solutions of multivalued backward stochastic differential equations

2021 ◽  
Author(s):  
Lucian Maticiuc ◽  
Aurel Rascanu
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Existence And Uniqueness ◽  
Lower Semicontinuous ◽  
Backward Stochastic Differential Equation ◽  
Stopping Time ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Variational Solutions ◽  
Convex Lower Semicontinuous Function

We prove the existence and uniqueness of the $L^{p}-$variational solution, with $p>1,$ of the fo\-llo\-wing multivalued backward stochastic differential equation with $p-$integrable data: \[ \left\{ \begin{array}[c]{l} -dY_{t}+\partial_{y}\Psi(t,Y_{t})dQ_{t}\ni H(t,Y_{t},Z_{t})dQ_{t}-Z_{t}dB_{t},\;0\leq t<\tau,\\[0.2cm] Y_{\tau}=\eta, \end{array} \right. \] where $\tau$ is a stopping time, $Q$ is a progressively measurable increasing continuous stochastic process and $\partial_{y}\Psi$ is the subdifferential of the convex lower semicontinuous function $y\mapsto\Psi(t,y).$

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