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Differentiability of Product Measures

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  • Heidergott, B.

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Leahu, H.

Abstract

In this paper, we study cost functions over a finite collection of random variables. For this type of models, a calculus of differentiation is developed that allows to obtain a closed-form expression for derivatives, where “differentiation” has to be understood in the weak sense. The techniques for establishing the results is new and establish an interesting link between functional analysis and gradient estimation. By establishing a product rule of weak analyticity, Taylor series approximations of finite products can be established. In particular, from characteristics of the individual probability measures a lower bound, i.e., domain of convergence can be established for the set of parameter values for which the Taylor series converges to the true value. Applications of our theory to the ruin problem from insurance mathematics and to stochastic activity networks arising in project evaluation review technique are provided.

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Bibliographic Info

Paper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0005.

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Date of creation: 2008
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Handle: RePEc:dgr:vuarem:2008-5

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References

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  1. Heidergott, Bernd & Vazquez-Abad, Felisa J. & Volk-Makarewicz, Warren, 2008. "Sensitivity estimation for Gaussian systems," European Journal of Operational Research, Elsevier, vol. 187(1), pages 193-207, May.
  2. Felisa J. Vazquez-Abad & Bernd Heidergott, 2003. "Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation," Tinbergen Institute Discussion Papers 03-057/4, Tinbergen Institute.
  3. Bernd Heidergott & Arie Hordijk & Miranda van Uitert, 2005. "Series Expansions for Finite-State Markov Chains," Tinbergen Institute Discussion Papers 05-086/4, Tinbergen Institute.
  4. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of all policies in Markov decision chains with a Borel state space and unbounded rewards," Computational Statistics, Springer, vol. 50(3), pages 421-448, December.
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Cited by:
  1. Akgun, A.A. & Baycan Levent, T. & Nijkamp, P., 2011. "The engine of sustainable rural development: Embeddedness of entrepreneurs in rural Turkey," Serie Research Memoranda 0008, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  2. Baycan, T. & Nijkamp, P., 2011. "A socio-economic impact analysis of cultural diversity," Serie Research Memoranda 0012, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Berg, V.A.C. van den, 2012. "Step tolling with price sensitive demand: Why more steps in the toll makes the consumer better off," Serie Research Memoranda 0003, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  4. Abbas, K. & Heidergott, B.F. & Aissani, D., 2011. "A Taylor series expansion approach to the functional approximation of finite queues," Serie Research Memoranda 0049, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. Nijkamp, P. & Cohen, G., 2011. "Opportunities and pitfalls of local e-democracy," Serie Research Memoranda 0023, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Nunes, P.A.L.D. & Nijkamp, P., 2011. "Biodiversity: Economic perspectives," Serie Research Memoranda 0002, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  7. Koomen, E., 2011. "Indicators of rural vitality. A GIS-based analysis of socio-economic development of the rural Netherlands," Serie Research Memoranda 0050, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  8. Kangasharju, A. & Tavera, C. & Nijkamp, P., 2011. "Regional growth and unemployment. The validity of Okun's law for the Finnish regions," Serie Research Memoranda 0006, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  9. Bernd Heidergott & Arie Hordijk & Haralambie Leahu, 2009. "Strong bounds on perturbations," Computational Statistics, Springer, vol. 70(1), pages 99-127, August.
  10. Bruinsma, F.R. & Kourtit, K. & Nijkamp, P., 2011. "Tourism, culture and e-services: Evaluation of e-services packages," Serie Research Memoranda 0016, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  11. Akgun, A.A. & Leeuwen, E.S. van & Nijkamp, P., 2011. "A systemic perspective on multi-stakeholder sustainable development strategies," Serie Research Memoranda 0009, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  12. Batabyal, A.A. & Nijkamp, P., 2011. "A Schumpeterian model of entrepreneurship, innovation, and regional economic growth," Serie Research Memoranda 0007, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  13. Akgun, A.A. & Baycan, T. & Nijkamp, P., 2011. "Repositioning rural areas as promising future hot spots," Serie Research Memoranda 0013, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  14. Diogo, V. & Koomen, E. & Hilst, F. van der, 2012. "Second generation biofuel production in the Netherlands. A spatially-explicit exploration of the economic viability of a perennial biofuel crop," Serie Research Memoranda 0004, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  15. Gulumser, A.A. & Baycan, T. & Nijkamp, P., 2011. "Measuring regional creative capacity: A literature review for rural-specific approaches," Serie Research Memoranda 0015, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  16. Kourtit, K. & Nijkamp, P., 2011. "Strangers on the move. Ethnic entrepreneurs as urban change actors," Serie Research Memoranda 0004, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  17. Bakens, J. & Nijkamp, P., 2011. "Lessons from migration impact analysis," Serie Research Memoranda 0022, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  18. Gulumser, A.A. & Baycan, T. & Nijkamp, P., 2011. "Business dynamics as the source of counterurbanisation: An empirical analysis of Turkey," Serie Research Memoranda 0021, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  19. Takashashi, Y. & Nijkamp, P., 2011. "Multifunctional agricultural land use in a sustainable world. Design and simulation of an agricultural economy model," Serie Research Memoranda 0001, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  20. Leeuwen, E.S. van & Nijkamp, P. & Rietveld, P., 2011. "Climate change: From global concern to regional challenge," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  21. Gulumser, A.A. & Baycan Levent, T. & Nijkamp, P. & Poot, H.J., 2012. "The role of local and newcomer entrepreneurs in rural development: A comparative meta-analytic study," Serie Research Memoranda 0001, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  22. Bernd Heidergott & Warren Volk-Makarewicz, 2013. "A Measure-Valued Differentiation Approach to Sensitivity Analysis of Quantiles," Tinbergen Institute Discussion Papers 13-082/III, Tinbergen Institute.
  23. Nijkamp, P. & Bruinsma, F.R. & Kourtit, K. & Leeuwen, E.S. van, 2011. "Supply of and demand for e-services in the cultural sector: Combining top-down and bottom-up perspectives," Serie Research Memoranda 0017, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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