Andreas J Novak
University of Vienna, Business Administration, Faculty Member
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In this paper we study how the scientific production of a representative researcher develops over his/her career. Using Pontryagin’s maximum principle we derive the optimal capital accumulation over the life cycle of a scientist. In... more
In this paper we study how the scientific production of a representative researcher develops over his/her career. Using Pontryagin’s maximum principle we derive the optimal capital accumulation over the life cycle of a scientist. In particular, we are able to identify two regimes of human capital accumulation (say intensive versus normal) and to characterize their optimality depending on the initial human capital level. The paper includes a formal proof of the negative impact of the obscolescence rate as well as the discount rate on human capital production and we show that this reduction is largest at earlier ages.
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This paper studies a three player hierarchical differential game (with a large country, a small country, and a terrorist organization), to analyze the actual European refugee situation. Terrorists may enter Europe as refugees, taking... more
This paper studies a three player hierarchical differential game (with a large country, a small country, and a terrorist organization), to analyze the actual European refugee situation. Terrorists may enter Europe as refugees, taking advantage of the Open Door Policy, to attack both countries. There are two scenarios: myopia and full awareness. Countries are myopic when they ignore each other’s security efforts, and the terrorist group only considers the weakest link’s security efforts. A comparison between the scenarios shows that for an extremely impatient large country, full awareness yields a greater level of security effort for the large country, a greater level of security effort for the small country, and more terrorist attacks. This is, however, an unstable equilibrium. The full awareness model with a patient large country is stable and lies in between the previous model and the myopic model. Although it yields larger investments in security, this still results in more terro...
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This is one of the first papers that links population growth, education, and institutional change within a dynamic optimization. The basic premise is, following interesting papers of Boucekkine with different co-authors dealing with the... more
This is one of the first papers that links population growth, education, and institutional change within a dynamic optimization. The basic premise is, following interesting papers of Boucekkine with different co-authors dealing with the Arab Spring, that elites manage first the ruling and then the transition to a ‘democratic’ government. We are less optimistic concerning the economic efficiency of domestic resource use and, more importantly, extend this framework by accounting for (endogenous) population growth. These extensions render the survival of any elite much less feasible than without population growth. Only a (cynical) elite worrying about the size of the population allows for a long-run and interior outcome. Therefore, the rulers and the elite have to account for a second phase in which they lose control over a country’s (financial) resources. If the elite lacks sufficient stakes in the second phase, it will ‘take the money and run’, i.e., no investment, at least close to ...
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Ancient Chinese history reveals many examples of a cyclical pattern of social development connected with the rise and the decline of dynasties. In this paper, a possible explanation of the periodic alternation between despotism and... more
Ancient Chinese history reveals many examples of a cyclical pattern of social development connected with the rise and the decline of dynasties. In this paper, a possible explanation of the periodic alternation between despotism and anarchy by a dynamic game between the rulers and the bandits is offered. The third part of the society, the farmers, are dealt with as
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"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the... more
"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the teacher/student ratio imply nonlinearities which are substantial enough to generate erratic behaviour of the time paths. The main message is that chaos in educational planning may result from assumptions which are indeed qualitatively realistic but which are quantitatively exaggerated." (SUMMARY IN FRE)
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The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced... more
The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced by Petrarch and his platonic mistress Laura. Recently, attempts have been made to model these emotional swings by catastrophe theory or nonlinear differential equations. This paper takes a
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In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic... more
In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic fluctuations of the consumption rate, the habit and the threshold. It turns out that both a low adjustment rate of the threshold as well
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Research Interests: Cannibalism and Predation
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"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the... more
"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the teacher/student ratio imply nonlinearities which are substantial enough to generate erratic behaviour of the time paths. The main message is that chaos in educational planning may result from assumptions which are indeed qualitatively realistic but which are quantitatively exaggerated." (SUMMARY IN FRE)
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Frequently, parameter estimation is preceded by a data-driven model selection procedure. In such a case traditional distribution theory based on the assumption of an a priori given model is no longer valid. In Pötscher (1991) the... more
Frequently, parameter estimation is preceded by a data-driven model selection procedure. In such a case traditional distribution theory based on the assumption of an a priori given model is no longer valid. In Pötscher (1991) the asymptotic distribution of estimators that are preceded by model selection has been studied. In this paper we study the small sample distribution and, in
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In this paper, we analyze the joint determination of optimal consumption and allocation of time between learning (accumulation of human capital), working for wages (used for consumption and accumulation of financial capital), and leisure.... more
In this paper, we analyze the joint determination of optimal consumption and allocation of time between learning (accumulation of human capital), working for wages (used for consumption and accumulation of financial capital), and leisure. Using Hopf bifurcation theory, we are able to show that cyclical training, working, leisuring, and consumption are optimal under certain constellations of parameters.
Research Interests: Applied Mathematics, Optimal Control, Modeling, Consumer Behavior, Human Capital, and 12 moreUtility Theory, Bifurcation theory, Learning, Working Time, Life Cycle, Maximization, Mathematical Model, Numerical Analysis and Computational Mathematics, Life Cycle Model, Electrical And Electronic Engineering, Hopf Bifurcation, and Limit Cycle
The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced... more
The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced by Petrarch and his platonic mistress Laura. Recently, attempts have been made to model these emotional swings by catastrophe theory or nonlinear differential equations. This paper takes a
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A non-linear version of Parlar's production and marketing model is analysed. The optimal production and advertising policies are derived using the Maximum Principle. A stability analysis or the canonical... more
A non-linear version of Parlar's production and marketing model is analysed. The optimal production and advertising policies are derived using the Maximum Principle. A stability analysis or the canonical system is carried out to determine the behaviour of production and marketing decisions over time. As the main result we show that the model might exhibit stable limit cycles as optimal
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A new optimal control model of chemotherapeutic cancer treatment is presented including both the number of cancer cells and the level of toxicity as state variables. It is shown that under certain conditions, periodic drug administration... more
A new optimal control model of chemotherapeutic cancer treatment is presented including both the number of cancer cells and the level of toxicity as state variables. It is shown that under certain conditions, periodic drug administration is optimal. Although the model is highly stylized and too simple to describe realistic chemotherapeutic treatment patterns, it may be seen as a first
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ABSTRACT We consider a semi-rational addiction model in which the user has perfect foresight over all things within the user’s control, but not necessarily with respect to exogenous parameter shocks, e.g., those stemming from changes in... more
ABSTRACT We consider a semi-rational addiction model in which the user has perfect foresight over all things within the user’s control, but not necessarily with respect to exogenous parameter shocks, e.g., those stemming from changes in national policy. We show that addictive substances are more likely to have state-dependent solution trajectories, and that in turn can create path dependence at the macro-policy level; in particular, legalization may be an irreversible experiment. Also, in this model, shifting from a nuanced policy that differentiates between high and low intensity users, to a tougher one where the government makes life hard for every user reduces initiation considerably. However, it also may have perverse effects. In particular, we show that making the policy tougher in this way could drive some people from a “happy” stable saddle point equilibrium with moderate consumption into increasing rather than reducing their consumption and addiction stock. So implementing zero tolerance policies may increase rather than reduce aggregate drug use, depending on the population’s distribution of parameter values and initial consumption stocks. Further, we consider the impact of announcing a policy change.