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Dynamic model of Loan Portfolio with Lévy Asset Prices
Šmíd, Martin
We generalize the well known Merton-Vasicek (KMV) model of a loan portfolio value in two ways: we assume a L' evy process of the debtors' assets' value (instead of the Gaussian one) and we model a dynamics of the portfolio value so that the debts may last several periods (instead of a single one). Our model is computable by simulation.
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Ramsey Stochastic Model via Multistage Stochastic Programming
Kaňková, Vlasta
Ramsey model belongs to ``classical" economic dynamic models. It has been (1928)originally constructed (with a farmer interpretation)in a deterministic setting. Later this model has been generalized to a stochastic version. Time horizont in the original deterministic model as well as in modified stochastic one can be considered finite or infinite. The contribution deals with the stochastic model and finite horizont. However, in spite of the classical approach to analyze it we employ a stochastic programming technique. This approach gives a possibility to employ well known results on stability and empirical estimates also in the case of Ramsey model. However, first, we introduce some confidence intervals. To obtain the new assertions we restrict our consideration mostly to the case when the ``underlying" random element follows autoregressive (or at least Markov) sequence.
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Risk-sensitive Ramsey Growth Model
Sladký, Karel
In this note we focus attention on risk-sensitive approach to an extended version of the Ramsey growth model. In contrast to the standard Ramsey model we assume that every splitting of production between consumption and capital accumulation is in uenced by some random factor governed by transition probabilities depending on the current value of the accumulated capital and possibly on some (costly) decisions. Moreover, we assume that also some additional (expensive) interventions of the decision maker are possible for changing the depreciation rate of the capital. Finding optimal policy of the extended model can be then formulated as nding optimal policy of a highly structured Markov decision process. Unfortunately usual optimization criteria for Markov decision processes cannot re ect variability-risk features of the problem. To this end, we indicate how nding policies yielding maximal risksensitive rewards.
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On statistical modeling of incidence of competing events, with application to labor mobility analysis
Volf, Petr
The contribution deals with the problem of competing risks (of competing events) in the statistical events occurrence analysis. In such a setting, one event excludes the occurrence of the other. Moreover, their latency may be dependent. Therefore, instead the analysis of marginal distributions (or intensities) of events, it is more convenient to model their real incidence, via so called incidence function. We present methods of such an incidence analysis and illustrate it on an example with unemployment data.
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