scholarly journals Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care

Risks ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 37
Author(s):  
Manuel L. Esquível ◽  
Gracinda R. Guerreiro ◽  
Matilde C. Oliveira ◽  
Pedro Corte Real
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Long Term Care ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Chain Model ◽  
Chain Process ◽  
Term Care ◽  
National Network

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.

Data Mining Technique Applied To DNA Sequencing

2015 ◽  
Vol 2 (7) ◽  
pp. 18
Author(s):  
R. Jamuna
Keyword(s):  
Data Mining ◽  
Dna Methylation ◽  
Markov Chain ◽  
Human Genome ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Effective Means ◽  
Cpg Islands ◽  
Chain Model ◽  
The Given

CpG islands (CGIs) play a vital role in genome analysis as genomic markers.  Identification of the CpG pair has contributed not only to the prediction of promoters but also to the understanding of the epigenetic causes of cancer. In the human genome [1] wherever the dinucleotides CG occurs the C nucleotide (cytosine) undergoes chemical modifications. There is a relatively high probability of this modification that mutates C into a T. For biologically important reasons the mutation modification process is suppressed in short stretches of the genome, such as ‘start’ regions. In these regions [2] predominant CpG dinucleotides are found than elsewhere. Such regions are called CpG islands. DNA methylation is an effective means by which gene expression is silenced. In normal cells, DNA methylation functions to prevent the expression of imprinted and inactive X chromosome genes. In cancerous cells, DNA methylation inactivates tumor-suppressor genes, as well as DNA repair genes, can disrupt cell-cycle regulation. The most current methods for identifying CGIs suffered from various limitations and involved a lot of human interventions. This paper gives an easy searching technique with data mining of Markov Chain in genes. Markov chain model has been applied to study the probability of occurrence of C-G pair in the given   gene sequence. Maximum Likelihood estimators for the transition probabilities for each model and analgously for the  model has been developed and log odds ratio that is calculated estimates the presence or absence of CpG is lands in the given gene which brings in many  facts for the cancer detection in human genome.

scholarly journals Long-Term Care Financing for an Aging Population: The Experience of Singapore

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 31-31
Author(s):  
Ngee Choon Chia ◽  
Huijun Cynthia Chen
Keyword(s):  
Long Term Care ◽  
Transition Probabilities ◽  
Aging Population ◽  
Elderly Male ◽  
Term Care ◽  
Cash Benefit ◽  
Opt Out ◽  
Insurance Rate ◽  
Long Term Care Insurance

Abstract Singapore has a rapidly aging population. Long-term care (LTC) is one of the largest financial risks facing elderly in Singapore. Singapore implemented Eldershield, a long-term care insurance scheme which provided defined cash benefit payouts in the event of severe disability; but capped at a maximum of six years. Eldershield enrolled people at age 40, but offered an opt-out option. As of 2015, 65% of those aged 40 to 83 opted to be covered by Eldershield, making Singapore as having the highest voluntary LTC insurance rate in the world. This paper uses an actuarial multi-state disability model and calibrates the transition probabilities and duration-of-stay at various health (disability) states to assess the adequacy and comprehensiveness of Eldershield. The time-limited cash benefit design in Eldershield helped defray about 13% of LTC costs. Removing the time cap will help defray 23% and 26% of the LTC costs for elderly male and female respectively. Furthermore, the simulation results demonstrate that relaxing the trigger benefit and having staggered payouts will improve the adequacy of long-term care insurance. The experience of Singapore’s LTC insurance offers insights into the challenges of designing an insurance that tends to occur at higher age and insuring against a cost that could range from zero to a significantly large sum over a long period. Even with the enhanced Careshield Life, which provides cash payouts for life, other policy designs, for example caregiver grants, may be needed to ensure more adequate financing of long-term care.

scholarly journals Will this search end up with booking? Modeling airline booking conversion of anonymous visitors

2020 ◽  
Vol 27 (2) ◽  
pp. 237-250
Author(s):  
Misuk Lee
Keyword(s):  
Markov Chain ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Distribution Channel ◽  
Stochastic Approach ◽  
Tourism Industry ◽  
Chain Model ◽  
Online Search ◽  
Clickstream Data ◽  
Content Type

Purpose Over the past two decades, online booking has become a predominant distribution channel of tourism products. As online sales have become more important, understanding booking conversion behavior remains a critical topic in the tourism industry. The purpose of this study is to model airline search and booking activities of anonymous visitors. Design/methodology/approach This study proposes a stochastic approach to explicitly model dynamics of airline customers’ search, revisit and booking activities. A Markov chain model simultaneously captures transition probabilities and the timing of search, revisit and booking decisions. The suggested model is demonstrated on clickstream data from an airline booking website. Findings Empirical results show that low prices (captured as discount rates) lead to not only booking propensities but also overall stickiness to a website, increasing search and revisit probabilities. From the decision timing of search and revisit activities, the author observes customers’ learning effect on browsing time and heterogeneous intentions of website visits. Originality/value This study presents both theoretical and managerial implications of online search and booking behavior for airline and tourism marketing. The dynamic Markov chain model provides a systematic framework to predict online search, revisit and booking conversion and the time of the online activities.

NATURAL HEDGING IN LONG-TERM CARE INSURANCE

2017 ◽  
Vol 48 (1) ◽  
pp. 233-274 ◽  
Author(s):  
Susanna Levantesi ◽  
Massimiliano Menzietti
Keyword(s):  
Value At Risk ◽  
Long Term Care ◽  
Transition Probabilities ◽  
Parametric Bootstrap ◽  
Conditional Value At Risk ◽  
Risk Minimization ◽  
Product Mix ◽  
Term Care ◽  
Hedging Strategies

AbstractWe investigate the application of natural hedging strategies for long-term care (LTC) insurers by diversifying both longevity and disability risks affecting LTC annuities. We propose two approaches to natural hedging: one built on a multivariate duration, the other on the Conditional Value-at-Risk minimization of the unexpected loss. Both the approaches are extended to the LTC insurance using a multiple state framework. In order to represent the future evolution of mortality and disability transition probabilities, we use the stochastic model of Cairns et al. (2009) with cohort effect under parameter uncertainty through a semi-parametric bootstrap procedure. We calculate the optimal level of a product mix and measure the effectiveness provided by the interaction of LTC stand alone, deferred annuity and whole-life insurance. We compare the results obtained by the two approaches and find that a natural hedging strategy for LTC insurers is attainable with a product mix of LTC and annuities, but including low proportion of LTC.

A new stochastic model of microsatellite evolution

1999 ◽  
Vol 36 (3) ◽  
pp. 621-631 ◽  
Author(s):  
Richard Durrett ◽  
Semyon Kruglyak
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Markov Chain Model ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Base Pairs ◽  
Microsatellite Evolution ◽  
Experimental Findings ◽  
Best Fit ◽  
Simple Sequence

We introduce a continuous-time Markov chain model for the evolution of microsatellites, simple sequence repeats in DNA. We prove the existence of a unique stationary distribution for our model, and fit the model to data from approximately 106 base pairs of DNA from fruit flies, mice, and humans. The slippage rates from the best fit for our model are consistent with experimental findings.

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