Multidimensional age-dependent branching processes allowing immigration: The limiting distribution

This paper continues the author's study of age-dependent branching processes allowing immigration. In this paper the multidimensional case is considered. A sufficient condition is obtained for the existence of a legitimate limiting distribution. Several corollaries are obtained, which generalize many of the results of the discrete theory and those of the one-dimensional continuous time model.

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Sharpe Ratios and Alphas in Continuous Time

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109000003902 ◽

2004 ◽

Vol 39 (1) ◽

pp. 103-114 ◽

Cited By ~ 18

Author(s):

Lars Tyge Nielsen ◽

Maria Vassalou

Keyword(s):

Continuous Time ◽

Sharpe Ratio ◽

Continuous Time Model ◽

Time Model ◽

Time Performance ◽

Optimal Portfolio Selection ◽

Dynamic Portfolio ◽

Sharpe Ratios ◽

The One ◽

Riskless Asset

AbstractThis paper proposes modified versions of the Sharpe ratio and Jensen's alpha, which are appropriate in a simple continuous-time model. Both are derived from optimal portfolio selection. The modified Sharpe ratio equals the ordinary Sharpe ratio plus half of the volatility of the fund. The modified alpha also differs from the ordinary alpha by a second-moment adjustment. The modified and the ordinary Sharpe ratios may rank funds differently. In particular, if two funds have the same ordinary Sharpe ratio, then the one with the higher volatility will rank higher according to the modified Sharpe ratio. This is justified by the underlying dynamic portfolio theory. Unlike their discrete-time versions, the continuous-time performance measures take into account that it is optimal for investors to change the fractions of their wealth held in the fund vs. the riskless asset over time.

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Limiting distribution for a simple model of order book dynamics

Open Mathematics ◽

10.2478/s11533-012-0098-3 ◽

2012 ◽

Vol 10 (6) ◽

Cited By ~ 1

Author(s):

Łukasz Kruk

Keyword(s):

Continuous Time ◽

Limit Order Book ◽

Limiting Distribution ◽

Model Parameters ◽

Order Book ◽

Continuous Time Model ◽

Time Model ◽

Limiting Behavior ◽

Bid Ask Spread ◽

Limit Orders

AbstractA continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.

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A continuous-time population model with poisson recruitment

Journal of Applied Probability ◽

10.2307/3212838 ◽

1976 ◽

Vol 13 (2) ◽

pp. 348-354 ◽

Cited By ~ 23

Author(s):

Sally I. McClean

Keyword(s):

Generating Function ◽

Continuous Time ◽

Population Model ◽

Probability Generating Function ◽

Joint Probability ◽

Limiting Distribution ◽

Continuous Time Model ◽

Time Model ◽

Second Moments ◽

Poisson Arrivals

A continuous-time model of a multigrade system is developed, which includes Poisson arrivals, interaction between grades and a leaving process. It therefore constitutes a continuous-time analogue of Pollard's hierarchical population model with Poisson recruitment. An expression is found for the first and second moments of grade size at any time. A general formulation of the joint probability generating function of the numbers in each grade is given, and the limiting distribution of grade size is shown to be Poisson.

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Absence of Cycles in Symmetric Neural Networks

Neural Computation ◽

10.1162/089976698300017430 ◽

1998 ◽

Vol 10 (5) ◽

pp. 1235-1249 ◽

Cited By ~ 6

Author(s):

Xin Wang ◽

Arun Jagota ◽

Fernanda Botelho ◽

Max Garzon

Keyword(s):

Discrete Time ◽

Continuous Time ◽

Necessary Conditions ◽

Continuous Time Model ◽

Time Model ◽

Discrete Time Model ◽

Asymptotic Dynamics ◽

The One ◽

Discretized Model ◽

Symmetric Networks

For a given recurrent neural network, a discrete-time model may have asymptotic dynamics different from the one of a related continuous-time model. In this article, we consider a discrete-time model that discretizes the continuous-time leaky integrat or model and study its parallel, sequential, block-sequential, and distributed dynamics for symmetric networks. We provide sufficient (and in many cases necessary) conditions for the discretized model to have the same cycle-free dynamics of the corresponding continuous-time model in symmetric networks.

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A continuous-time population model with poisson recruitment

Journal of Applied Probability ◽

10.1017/s0021900200094419 ◽

1976 ◽

Vol 13 (02) ◽

pp. 348-354 ◽

Cited By ~ 6

Author(s):

Sally I. McClean

Keyword(s):

Generating Function ◽

Continuous Time ◽

Population Model ◽

Probability Generating Function ◽

Joint Probability ◽

Limiting Distribution ◽

Continuous Time Model ◽

Time Model ◽

Second Moments ◽

Poisson Arrivals

A continuous-time model of a multigrade system is developed, which includes Poisson arrivals, interaction between grades and a leaving process. It therefore constitutes a continuous-time analogue of Pollard's hierarchical population model with Poisson recruitment. An expression is found for the first and second moments of grade size at any time. A general formulation of the joint probability generating function of the numbers in each grade is given, and the limiting distribution of grade size is shown to be Poisson.

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