Advanced Topics in Finance: Semi‐Markov Models

Janssen, Jacques; Manca, Oronzio; Manca, Raimondo

doi:10.1002/9781118578339.ch12

Cited by 2 publications

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“…The process that combines the transition times and the discrete mode is typically called a Markov renewal process [9], which motivated us to refer to these systems as stochastic hybrid systems with renewal transitions. This class of systems can be viewed as a special case of the SHS model in [5], which in turn is a special case of a piecewise deterministic process [4] and also a special case of a state-dependent jump-diffusion [6, sect.…”

Section: Introduction and Examplesmentioning

confidence: 99%

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

Antunes¹,

Hespanha²,

Silvestre³

2013

SIAM J. Control Optim.

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. (2013). Stochastic hybrid systems with renewal transitions : moment analysis with application to networked control systems with delays. SIAM Journal on Control and Optimization, 51(2), 1481-1499. DOI: 10.1137/12087623X General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract. We consider stochastic hybrid systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS. Moreover, we provide a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rate of decrease or increase at which statistical moments converge to zero or to infinity, respectively. We also discuss how, by computing the statistical moments, one can provide information about the probability distribution of the state of the SHS. The applicability of the results is illustrated in the analysis of a networked control problem with independently distributed intervals between data transmissions and delays.

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Section: Introduction and Examplesmentioning

confidence: 99%

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

Antunes¹,

Hespanha²,

Silvestre³

2013

SIAM J. Control Optim.

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“…Numerous examples of applications to areas such as reliability, insurance and finance were provided by Janssen (1999), Janssen and Manca (2006,2007) and Janssen and Limnios (2001), for instance. In such studies, it is most common to consider estimation methods assuming that a single realization of a semi-Markov process is observed over a finite time interval [0, τ ] whose length tends to infinity ( τ ↑ ∞).…”

Section: Introductionmentioning

confidence: 99%

Estimation in a Semi-Markov Transformation Model

Dabrowska¹

2012

The International Journal of Biostatistics

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Semi-Markov and modulated renewal processes provide a large class of multi-state models which can be used for analysis of longitudinal failure time data. In biomedical applications, models of this kind are often used to describe evolution of a disease and assume that patient may move among a finite number of states representing different phases in the disease progression. Several authors proposed extensions of the proportional hazard model for regression analysis of these processes. In this paper, we consider a general class of censored semi-Markov and modulated renewal processes and propose use of transformation models for their analysis. Special cases include modulated renewal processes with interarrival times specified using transformation models, and semi-Markov processes with with one-step transition probabilities defined using copula-transformation models. We discuss estimation of finite and infinite dimensional parameters and develop an extension of the Gaussian multiplier method for setting confidence bands for transition probabilities and related parameters. A transplant outcome data set from the Center for International Blood and Marrow Transplant Research is used for illustrative purposes.

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Advanced Topics in Finance: Semi‐Markov Models

Cited by 2 publications

References 0 publications

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

Estimation in a Semi-Markov Transformation Model

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