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2015, 2015(special): 159-168. doi: 10.3934/proc.2015.0159

Stochastic control of individual's health investments

1. 

Leibniz Institute of Agricultural Development in Transition Economies, Theodor-Lieser-Street 2, Halle (Saale), 06120, Germany, Germany

2. 

Martin-Luther-University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Street 5, Halle (Saale), 06120, Germany

Received  September 2014 Revised  August 2015 Published  November 2015

Grossman's health investment model has been one of the most important developments in health economics. However, the model's derived demand function for medical care predicts the demand for medical care to increase if the individual's health status increases. Yet, empirical studies indicate the opposite relationship. Therefore, this study improves the informative value of the health investment model by introducing a reworked Grossman model, which assumes a more realistic Cobb-Douglas health investment function with decreasing returns to scale. Because we introduced uncertainty surrounding individual's health status the resulting dynamic utility maximization problem is tackled by optimal stochastic control theory.
Citation: Christine Burggraf, Wilfried Grecksch, Thomas Glauben. Stochastic control of individual's health investments. Conference Publications, 2015, 2015 (special) : 159-168. doi: 10.3934/proc.2015.0159
References:
[1]

M. Grossman, The demand for health: a theoretical and empirical investigation,, National Bureau of Economic Research, (1972).   Google Scholar

[2]

M. Grossman, The human capital model,, in Handbook of health economics (eds. A. J. Culyer and J. P. Newhouse) Elsevier Science, (2000).   Google Scholar

[3]

P. Zweifel, The Grossman model after 40 years,, Eur. J. Health Econ., 13 (2012), 677.   Google Scholar

[4]

U. G. Gerdtham, M. Johannesson, L. Lundberg and D. G. L. Isacson, The demand for health: results from new measures of health capital,, Eur. J. Health Econ., 15 (1999), 501.   Google Scholar

[5]

A. Wagstaff, The demand for health: Some new empirical evidence,, J. Health Econ., 53 (1986), 195.   Google Scholar

[6]

M. Erbsland, W. Ried and V. Ulrich, Health, health care, and the environment: Econometric evidence from German micro data,, Health Econ., 4 (1995), 169.   Google Scholar

[7]

I. Ehrlich and H. Chuma, A Model of the Demand for Longevity and the Value of Life Extension,, J. Pol. Econ., 98 (1990), 761.   Google Scholar

[8]

R. Kaestner, The Grossman model after 40 years: A reply to Peter Zweifel,, Eur. J. Health Econ., 14 (2013), 357.   Google Scholar

[9]

T. J. Galama, P. Hullegie, E. Meijer and S. Outcault, Is there empirical evidence for decreasing returns to scale in a health capital model?,, Health Econ., 21 (2012), 1080.   Google Scholar

[10]

A. Laporte, Should the Grossman model retain its iconic status in health economics?,, CCHE/CCES Working paper, (2014).   Google Scholar

[11]

V. Dardanoni and A. Wagstaff, Uncertainty, inequalities in health and the demand for health ,, J. Health Econ., 6 (1987), 283.   Google Scholar

[12]

G. Picone, M. Uribe, R. M. Wilson, The effect of uncertainty on the demand for medical care, health capital and wealth,, J. Health Econ., 17 (1998), 171.   Google Scholar

[13]

L. S. Pontryagin, W. Boltjanski, R. V. Gamkrelidze and E. F. Mishchenko, Mathematische Theorie optimaler Prozesse, (German) [Mathematical Theory of Optimal Processes],, $2^{nd}$ edition, (1967).   Google Scholar

[14]

A. A. Leibowitz, The demand for health and health concerns after 30 years,, J. Health Econ., 23 (2004), 663.   Google Scholar

[15]

A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, (German) [Foundations of the theory of probablity],, $2^{nd}$ edition, (1967).   Google Scholar

[16]

A. G. Malliaris and W. A. Brock, Stochastic methods in economics and finance,, Elsevier/North-Holland, (1982).   Google Scholar

[17]

J. M. Bismut, Conjugate convex functions in optimal stochastic control,, J. Math. Anal. Appl., 44 (1973), 384.   Google Scholar

[18]

W. Ried, Comparative dynamic analysis of the full Grossman model,, J. Health Econ., 17 (1998), 383.   Google Scholar

[19]

M. Kuhn, S. Wrzaczek, A. Prskawetz, G. Feichtinger, Externalities in a Life-Cycle Model with Endogenous Survival,, J. Math. Econ., 47 (2011), 627.   Google Scholar

[20]

M. E. Yaari, Uncertain lifetime, life insurance, and the theory of the consumer,, Rev. Econ. Stud., 32 (1965), 137.   Google Scholar

[21]

W. H. Fleming, R. W. Rishel, Deterministic and stochstic optimal control,, Springer, (1975).   Google Scholar

show all references

References:
[1]

M. Grossman, The demand for health: a theoretical and empirical investigation,, National Bureau of Economic Research, (1972).   Google Scholar

[2]

M. Grossman, The human capital model,, in Handbook of health economics (eds. A. J. Culyer and J. P. Newhouse) Elsevier Science, (2000).   Google Scholar

[3]

P. Zweifel, The Grossman model after 40 years,, Eur. J. Health Econ., 13 (2012), 677.   Google Scholar

[4]

U. G. Gerdtham, M. Johannesson, L. Lundberg and D. G. L. Isacson, The demand for health: results from new measures of health capital,, Eur. J. Health Econ., 15 (1999), 501.   Google Scholar

[5]

A. Wagstaff, The demand for health: Some new empirical evidence,, J. Health Econ., 53 (1986), 195.   Google Scholar

[6]

M. Erbsland, W. Ried and V. Ulrich, Health, health care, and the environment: Econometric evidence from German micro data,, Health Econ., 4 (1995), 169.   Google Scholar

[7]

I. Ehrlich and H. Chuma, A Model of the Demand for Longevity and the Value of Life Extension,, J. Pol. Econ., 98 (1990), 761.   Google Scholar

[8]

R. Kaestner, The Grossman model after 40 years: A reply to Peter Zweifel,, Eur. J. Health Econ., 14 (2013), 357.   Google Scholar

[9]

T. J. Galama, P. Hullegie, E. Meijer and S. Outcault, Is there empirical evidence for decreasing returns to scale in a health capital model?,, Health Econ., 21 (2012), 1080.   Google Scholar

[10]

A. Laporte, Should the Grossman model retain its iconic status in health economics?,, CCHE/CCES Working paper, (2014).   Google Scholar

[11]

V. Dardanoni and A. Wagstaff, Uncertainty, inequalities in health and the demand for health ,, J. Health Econ., 6 (1987), 283.   Google Scholar

[12]

G. Picone, M. Uribe, R. M. Wilson, The effect of uncertainty on the demand for medical care, health capital and wealth,, J. Health Econ., 17 (1998), 171.   Google Scholar

[13]

L. S. Pontryagin, W. Boltjanski, R. V. Gamkrelidze and E. F. Mishchenko, Mathematische Theorie optimaler Prozesse, (German) [Mathematical Theory of Optimal Processes],, $2^{nd}$ edition, (1967).   Google Scholar

[14]

A. A. Leibowitz, The demand for health and health concerns after 30 years,, J. Health Econ., 23 (2004), 663.   Google Scholar

[15]

A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, (German) [Foundations of the theory of probablity],, $2^{nd}$ edition, (1967).   Google Scholar

[16]

A. G. Malliaris and W. A. Brock, Stochastic methods in economics and finance,, Elsevier/North-Holland, (1982).   Google Scholar

[17]

J. M. Bismut, Conjugate convex functions in optimal stochastic control,, J. Math. Anal. Appl., 44 (1973), 384.   Google Scholar

[18]

W. Ried, Comparative dynamic analysis of the full Grossman model,, J. Health Econ., 17 (1998), 383.   Google Scholar

[19]

M. Kuhn, S. Wrzaczek, A. Prskawetz, G. Feichtinger, Externalities in a Life-Cycle Model with Endogenous Survival,, J. Math. Econ., 47 (2011), 627.   Google Scholar

[20]

M. E. Yaari, Uncertain lifetime, life insurance, and the theory of the consumer,, Rev. Econ. Stud., 32 (1965), 137.   Google Scholar

[21]

W. H. Fleming, R. W. Rishel, Deterministic and stochstic optimal control,, Springer, (1975).   Google Scholar

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