Continuous-time stochastic modelling of capital adequacy ratios for banks

2006 ◽  
Vol 22 (1) ◽  
pp. 41-71 ◽  
Author(s):  
Casper H. Fouche ◽  
J. Mukuddem-Petersen ◽  
M. A. Petersen
Keyword(s):  
Continuous Time ◽  
Stochastic Modelling ◽  
Capital Adequacy

Incorporating concepts from physical theory into stochastic modelling of urban runoff pollution

1998 ◽  
Vol 37 (1) ◽  
pp. 179-185
Author(s):  
Morten Grum
Keyword(s):  
Stochastic Model ◽  
Continuous Time ◽  
Measurement Errors ◽  
Physical Theory ◽  
Oxygen Demand ◽  
Stochastic Modelling ◽  
Urban Runoff ◽  
Primary Input ◽  
Deterministic Modelling ◽  
Runoff Pollution

On evaluating the present or future state of integrated urban water systems, sewer drainage models, with rainfall as primary input, are often used to calculate the expected return periods of given detrimental acute pollution events and the uncertainty thereof. The model studied in the present paper incorporates notions of physical theory in a stochastic model of water level and particulate chemical oxygen demand (COD) at the overflow point of a Dutch combined sewer system. A stochastic model based on physical mechanisms has been formulated in continuous time. The extended Kalman filter has been used in conjunction with a maximum likelihood criteria and a non-linear state space formulation to decompose the error term into system noise terms and measurement errors. The bias generally obtained in deterministic modelling, by invariably and often inappropriately assuming all error to result from measurement inaccuracies, is thus avoided. Continuous time stochastic modelling incorporating physical, chemical and biological theory presents a possible modelling alternative. These preliminary results suggest that further work is needed in order to fully appreciate the method's potential and limitations in the field of urban runoff pollution modelling.

scholarly journals Weather Derivatives and Stochastic Modelling of Temperature

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Fred Espen Benth ◽  
Jūratė Šaltytė Benth
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
Stochastic Modelling ◽  
Temperature Data ◽  
Option Prices ◽  
Futures Prices ◽  
Degree Days ◽  
Temperature Dynamics ◽  
Heating Degree Days ◽  
Model Temperature

We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.

Superposition of Interacting Aggregated Continuous-Time Markov Chains

1997 ◽  
Vol 29 (01) ◽  
pp. 56-91
Author(s):  
Frank Ball ◽  
Robin K. Milne ◽  
Ian D. Tame ◽  
Geoffrey F. Yeo
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Stochastic Modelling ◽  
The Other ◽  
Transition Rates ◽  
Matrix Methods ◽  
Joint Distributions ◽  
Invariant Distributions ◽  
Reliability Modelling ◽  
Finite Markov Chains

Consider a system of interacting finite Markov chains in continuous time, where each subsystem is aggregated by a common partitioning of the state space. The interaction is assumed to arise from dependence of some of the transition rates for a given subsystem at a specified time on the states of the other subsystems at that time. With two subsystem classes, labelled 0 and 1, the superposition process arising from a system counts the number of subsystems in the latter class. Key structure and results from the theory of aggregated Markov processes are summarized. These are then applied also to superposition processes. In particular, we consider invariant distributions for the level m entry process, marginal and joint distributions for sojourn-times of the superposition process at its various levels, and moments and correlation functions associated with these distributions. The distributions are obtained mainly by using matrix methods, though an approach based on point process methods and conditional probability arguments is outlined. Conditions under which an interacting aggregated Markov chain is reversible are established. The ideas are illustrated with simple examples for which numerical results are obtained using Matlab. Motivation for this study has come from stochastic modelling of the behaviour of ion channels; another application is in reliability modelling.

Superposition of Interacting Aggregated Continuous-Time Markov Chains

1997 ◽  
Vol 29 (1) ◽  
pp. 56-91 ◽  
Author(s):  
Frank Ball ◽  
Robin K. Milne ◽  
Ian D. Tame ◽  
Geoffrey F. Yeo
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Stochastic Modelling ◽  
The Other ◽  
Transition Rates ◽  
Matrix Methods ◽  
Joint Distributions ◽  
Invariant Distributions ◽  
Reliability Modelling ◽  
Finite Markov Chains

Consider a system of interacting finite Markov chains in continuous time, where each subsystem is aggregated by a common partitioning of the state space. The interaction is assumed to arise from dependence of some of the transition rates for a given subsystem at a specified time on the states of the other subsystems at that time. With two subsystem classes, labelled 0 and 1, the superposition process arising from a system counts the number of subsystems in the latter class. Key structure and results from the theory of aggregated Markov processes are summarized. These are then applied also to superposition processes. In particular, we consider invariant distributions for the level m entry process, marginal and joint distributions for sojourn-times of the superposition process at its various levels, and moments and correlation functions associated with these distributions. The distributions are obtained mainly by using matrix methods, though an approach based on point process methods and conditional probability arguments is outlined. Conditions under which an interacting aggregated Markov chain is reversible are established. The ideas are illustrated with simple examples for which numerical results are obtained using Matlab. Motivation for this study has come from stochastic modelling of the behaviour of ion channels; another application is in reliability modelling.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Hierarchical Bayesian continuous time dynamic modeling.

2018 ◽  
Vol 23 (4) ◽  
pp. 774-799 ◽  
Author(s):  
Charles C. Driver ◽  
Manuel C. Voelkle
Keyword(s):  
Dynamic Modeling ◽  
Continuous Time ◽  
Hierarchical Bayesian ◽  
Time Dynamic
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