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Author
Delong Łukasz (Warsaw School of Economics, Poland)
Title
Applications of backward stochastic differential equations to insurance and finance
Source
Roczniki Kolegium Analiz Ekonomicznych / Szkoła Główna Handlowa, 2010, nr 21, s. 11-26, bibliogr. 15 poz.
Issue title
Zagadnienia aktuarialne : teoria i praktyka
Keyword
Równania różniczkowe, Matematyka ubezpieczeniowa, Matematyka finansowa
Differential equations, Insurance mathematics, Financial mathematics
Note
streszcz., summ.
Abstract
W pracy tej rozważamy wsteczne stochastyczne równania różniczkowe oraz ich zastosowania w ubezpieczeniach i finansach. Dwa główne obszary zastosowań obejmują: wycenę zobowiązań i miary ryzyka oraz problemy optymalizacyjne w teorii sterowania stochastycznego. Naszym celem jest pokazanie, że wsteczne stochastyczne równania różniczkowe, mimo iż wymagają znajomości zaawansowanego matematycznego aparatu, mogą być pomocne przy rozwiązaniu rzeczywistych problemów. (abstrakt oryginalny)

In this paper we deal with backward stochastic differential equations and give examples of their applications to insurance and finance. There are two major fields of applications. The first area concerns pricing and risk measures, the second deals with optimal control problems and optimization. Our aim is to show that backward stochastic differential equations,despite its mathematical complexity, are intuitive and can help in solving real life problems. Keywords: backward stochastic differential equation, Choquet expectation, f-expectation, market consistent valuation, quadratic hedging, unit-linked products. (original abstract)
Accessibility
The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
The Main Library of Poznań University of Economics and Business
The Main Library of the Wroclaw University of Economics
Bibliography
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  1. Barrieu P., El Karoui, N. (2005) Pricing, hedging and optimally designing derivatives via minimization of risk measures. preprint.
  2. Blanchert-Scalliet C., Eyraud-Loisel A., Royer-Carenzi M., (2008) Hedging of defaultable contingent claims using BSDE with uncertain time horizon, preprint.
  3. Delong Ł., (2009) An optimal investment strategy for a strearn of liabilities driven by a step process in a financial market driven by a Levy process, Insurance: Mathematics and Economics, in press.
  4. Delong Ł,. (2009) Applications of backward stochastic differential eąuations with time delayed generators to insurance, submited.
  5. Delong Ł., Imkeller P., (2009) Backward stochastic differential eąuations with time delayed generators - results and counterezamples, The Annals of Aplied Probability 20, 1512-1536.
  6. El Karoui N., Peng S., Quenez M.C., (1997) Backward stochastic differential eąuations in finance, Mathematical Finance 7, 1-71.
  7. Hu, Y., Imkeller P., Muller M., (2005) Utility maximization in incomplete markets, Annals of Applied Probability 15, 1691-1712.
  8. Imkeller P., (2008) Malliavin's Calculus and Applications in Stochastic Control and Finance, IM PAN Lectures Notes, Warsaw.
  9. Karatzas I., Shreve S., (1988) Brownian Motion and Stochastic Calculus, Springer-Verlag.
  10. Kobylański M., (2000) Backward stochastic differential equations and partial differential equations with quadratic growth, Annals of Probabability 28, 558-602.
  11. Peng S., (1997) Backward SDE and related g-expectations, in Backward Stochastic Differential Eąuations, eds. El-Karoui N., Mazliak L., Pitman Re-search Notes.
  12. Peng S., (2006) Modelling derivatives pricing mechanisms with their generating functions, preprint.
  13. Pardoux E., Peng S., (1990) Adapted solution of a backward stochastic differential equation, Systems Control Letters 14, 55-61.
  14. Wang S., (1996) Premium calculation by transforming the layer premium density, ASTIN Bulletin 26, 71-92.
  15. Yaari M. E., (1987) The dual theory of choice under risk, Econometrica 55, 95-115.
Cited by
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ISSN
1232-4671
Language
eng
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