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prof. dr hab. inż. Lesław Gajek

L.G.

Full Professor

The Division of Insurance and Capital Markets

Room:164

Phone: (+48) 42 631-36-34

e-mail: gal@p.lodz.pl

 

Treść (rozbudowana)
PhD students
  • Łukasz Kuciński, Optimal surplus management in insurance (IM PAN), 2015
  • Elżbieta Krajewska, Geometryczna teoria immunizacji na rynkach niezupełnych, 2015
  • Marcin Rudź, Wybrane oszacowania prawdopodobieństwa ruiny (IM PAN), 2013
  • Violetta Lipińska, Zastosowanie nierówności informacyjnych w predykcji minimaksowej, 2007
  • Andrzej Okolewski, Oszacowanie funkcjonałów statystyk pozycyjnych i rekordowych, 2000
  • Piotr Pokarowski, Lasy skierowane i algorytmy związane z łańcuchami Markowa, 1998
  • Adam Lenic, Metody projekcji nieparametrycznej estymacji gęstości, 1995
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Books
  • Lesław Gajek, Podstawy ubezpieczeń majątkowych. Modele i metody aktuarialne, PWN, (80 pkt.), 2022
  • Lesław Gajek, K. M. Ostaszewski, Financial Risk Management of Pension Plans, Elsevier, Amsterdam, New York, 2004
  • Lesław Gajek, K. M. Ostaszewski, Plany emerytalne. Zarządzanie aktywami i zobowiązaniami, WNT, Warszawa, 2002
  • Lesław Gajek, Marek Kałuszka, Wnioskowanie statystyczne. Modele i metody (2 wydanie 1994, 3 wydanie (poprawione i uzupełnione) 1996, 4 wydanie (rozszerzone) 2000), WNT, Warszawa, 1993
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Scientific publications
  • Gajek L., Krajewska E.  Robust portfolio choice under the interest rate uncertainty. OPTIMIZATION (70 pkt.) ISSN: 0233-1934, vol. 71, no. 9, rok 2022, str. 2727-2747.
  • Lesław Gajek, Marcin Rudź, General methods for bounding multidimensional ruin probabilities in regime-switching models, Stochastics-An International Journal of Probability and Stochastic Processes (70 pkt.), 93 (5) (2021), 764-779
  • Lesław Gajek, Marcin Rudź, Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model, Methodology and Computing in Applied Probability (70 pkt.), 22 (2020), 1507–1528
  • Lesław Gajek, Marcin Rudź, Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model, Methodology and Computing in Applied Probability (70 pkt.), 22 (2020), 1493–1506
  • Lesław Gajek, Elżbieta Krajewska, Approximating sums of products of dependent random variables, Statistics and Probability Letters (70 pkt.), 164 (art. 108803) (2020), 8 pp.
  • Lesław Gajek, Marcin Rudź, Banach Contraction Principle and ruin probabilities in regime-switching models, Insurance: Mathematics & Economics (30 pkt.), 80 (2018), 45-53, JCR
  • Lesław Gajek, Marcin Rudź, Deficit distributions at ruin in a regime-switching Sparre Andersen model, Journal of Applied Analysis (9 pkt.), 24 (1) (2018), 99-107
  • Lesław Gajek, Elżbieta Krajewska, Balance-sheet interest rate risk: a weighted L^p approach, Journal of Risk (15 pkt.), 21 (1) (2018), 91-104, JCR
  • Lesław Gajek, Marcin Rudź, Risk-switching insolvency models, Roczniki Kolegium Analiz Ekonomicznych (9 pkt.), 51 (2018), 129-146
  • Lesław Gajek, Łukasz Kuciński, Complete discounted cash flow valuation, Insurance: Mathematics & Economics (30 pkt.), 73 (2017), 1-19, JCR
  • Lesław Gajek, Elżbieta Krajewska, Portfolio immunization under cone restrictions, Journal of Applied Analysis (9 pkt.), 23 (2) (2017), 127-135
  • Lesław Gajek, Marcin Rudź, A generalization of Gerber's inequality for ruin probabilities in risk-switching models, Statistics & Probability Letters (20 pkt.), 129 (2017), 236-240, JCR
  • Lesław Gajek, Elżbieta Krajewska, A new immunization inequality for random streams of assets, liabilities and interest rates, Insurance:Mathematics and Economics, 53 (2013), 624-631, JCR
  • Lesław Gajek, Wojciech Niemiro, Piotr Pokarowski, Optimal Monte Carlo integration with fixed relative precision, J. Complexity, 29 (2013), 4-26, JCR
  • Lesław Gajek, Marcin Rudź, Sharp approximations of ruin probabilities in the discrete time models, Scandinavian Actuarial Journal (20 pkt.), 2013 (5) (2013), 352-382, JCR
  • Lesław Gajek, Violetta Lipińska, Minimax inequality for the prediction risk, Math. Inequalities Appl., 13 (2010), 437-448, JCR
  • Lesław Gajek, P. Miś, J. Słowińska, Optimal streams of premiums in multiperiod credibility models, Appl. Math., 34 (2007), 223-235
  • Lesław Gajek, Violetta Lipińska, Sharp inequality for the Bayes prediction risk, Inequal. Th. Appl. Nova Sci. Publ., 5 (2006), 97-106
  • Lesław Gajek, Axiom of Solvency and portfolio immunization under random interest rates, Insurance: Math. Econom., 36 (2005), 317-328, JCR
  • Lesław Gajek, On the deficit distribution when the ruin occurs - discrete time model, Insurance: Math. Econom., 36 (2005), 13-24, JCR
  • Lesław Gajek, K. Ostaszewski, H.-J. Zwiesler, A Primer on Duration, Convexity, and Immunization, J. Actuar. Pract., 12 (2005), 59-82
  • Lesław Gajek, D. Zagrodny, Optimal reinsurance under general risk measures, Insurance Math. Econom., 34 (2004), 227-240, JCR
  • Lesław Gajek, D. Zagrodny, Reinsurance arrangements maximizing insurer's survival probability (uzyskała nagrodę The David Garrick Halmstad Prize w 2006 r.), J. Risk and Insurance, 71 (2004), 421- 436, JCR
  • Lesław Gajek, Andrzej Okolewski, Projection bounds on expectations of record statistics from restricted families, J. Statist. Plann. Inference, 110 (2003), 97-108, JCR
  • Lesław Gajek, Random fluctuation of the valuation of pension plans (in Polish), Acta Univ. Lodz., Folia Oeconomica, 162 (2002), 49-68
  • Lesław Gajek, Andrzej Okolewski, Sharp bounds on quasiconvex moments of generalized order statistics, J. Inequalities in Pure & Appl. Math., 2 (2001), Article 6
  • Lesław Gajek, K. Ostaszewski, Optimal funding of a liability, J. Insurance Issues, 24 (1 & 2) (2001), 17-29
  • Lesław Gajek, Andrzej Okolewski, Improved Steffensen type bounds on generalized moments of record statistics, Statist. Probab. Lett., 55 (2001), 205-212, JCR
  • Lesław Gajek, Marek Kałuszka, On the average return rate for a group of investment funds, Acta Univ. Lodz., Folia Oeconomica, 152 (2000), 161-171
  • Lesław Gajek, Jacek Jachymski, Piotr Pokarowski, The Tarski-Kantorovitch principle and the theory of iterated function systems, Bull. Austral. Math. Soc., 61 (2000), 247-261, JCR
  • Lesław Gajek, Andrzej Okolewski, Inequalities for generalized order statistics from some restricted family of distributions, Comm. Statist. Theory Methods, 29 (2000), 2427-2438, JCR
  • Lesław Gajek, D. Zagrodny, Insurer's optimal reinsurance strategies, Insurance Math. Econom., 27 (2000), 105-112, JCR
  • Lesław Gajek, Andrzej Okolewski, Sharp bounds on moments of generalized order statistics, Metrika, 52 (2000), 27-43, JCR
  • Lesław Gajek, Agnieszka Drwalewska, On localizing global Pareto solutions in a given convex set, Appl. Math., 26 (1999), 383-394
  • Lesław Gajek, K. Sobczyk, On composite stochastic processes and road vehicle response, Computational stochastic mechanics. Proceedings of the 3rd international conference (CSM'98) held on Santorini, Greece, June 14-17, 1998, (1999), 491-495
  • Kazimierz Sobczyk, Lesław Gajek, Marek Kałuszka, On composite stochastic processes and road vehicle response. Spanos, P. D. (ed.), Computational stochastic mechanics., Proceedings of the 3rd international conference (CSM'98) held on Santorini, Greece, June 14-17, 1998, Rotterdam: A. A. Balkema (1999), 491--495
  • Lesław Gajek, J. Mielniczuk, Long and short-range dependent sequences under exponential subordination, Statist. Probab. Lett., 43 (1999), 113-121, JCR
  • Lesław Gajek, B. Mizera-Florczak, Information inequalities for the minimax risk of sequential estimators, Appl. Math., 25 (1998), 85-100
  • Lesław Gajek, T. Rychlik, Projection method for moment bounds on order statistics from restricted families: II Independent case, Journal of Multivariate Analysis, 64 (1998), 156-182, JCR
  • Lesław Gajek, Andrzej Okolewski, Steffensen type inequalities for order and record statistics, Annales UMCS, Volume dedicated to Prof. D. Szynal, Vol. LI (1) (1997), 41-59
  • Lesław Gajek, T. Rychlik, Projection method for moment bounds on order statistics from restricted families: I Dependent case, Journal of Multivariate Analysis, 57 (1996), 156-174, JCR
  • Lesław Gajek, Marek Kałuszka, On some inequalities for L-unbiased estimators, Statistics and Decisions, 14 (1996), 177-197
  • Lesław Gajek, Marek Kałuszka, A. Lenic, The law of the iterated logarithm for Lp-norms of empirical processes, Statistics and Probability Letters, 28 (1996), 107-110, JCR
  • Lesław Gajek, Note on unbiased estimability of the larger of two mean values, Applicationes Mathematicae, 23 (1995), 239-245
  • Lesław Gajek, M. Bismarck, An upper bound for the power of a test, Communications in Statistics, Theory and Methods, 24 (1995), 813-828, JCR
  • Lesław Gajek, D. Zagrodny, Geometric variational principle.Different aspects of differentiability., Dissertationes Mathematicae, 340 (1995), 55-71, JCR
  • Lesław Gajek, D. Zagrodny, Geometric mean value theorems for the Dini derivative, J. Math. Anal. Appl., 191 (1995), 56-76, JCR
  • Lesław Gajek, Jacek Jachymski, Dariusz Zagrodny, Fixed point and approximate fixed point theorems for non-affine maps, Journal of Applied Analysis, 1 (1995), 205-211
  • Lesław Gajek, Jacek Jachymski, Dariusz Zagrodny, Projections, extendability of operators and the Gateaux derivative of the norm, Journal of Applied Analysis, 1 (1995), 29-38
  • Lesław Gajek, Marek Kałuszka, Nonexponential applications of a global Cramer-Rao inequality, Statistics, 26 (1995), 111-122, JCR
  • Lesław Gajek, Marek Kałuszka, Lower bounds for the asymptotic Bayes risk in the scale model (with an application to the second order minimax estimation), Ann. Statist., 22 (1994), 1831-1839, JCR
  • Lesław Gajek, E. Lenic, Moment inequalities for order and record statistics under restrictions on their distributions, Annales UMCS, Vol. XLVII (3) (1994), 27-34
  • Lesław Gajek, D. Zagrodny, Approximate necessary conditions for a locally weak Pareto optimality, Journal of Optimization, Theory and Applications, 82 (1994), 49-58, JCR
  • Lesław Gajek, D. Zagrodny, Weierstrass theorem for monotonically semicontinuous functions, Optimization, 29 (1994), 199-203, JCR
  • Lesław Gajek, A. Lenic, An approximate necessary condition for the optimal bandwidth selector in kernel density estimation, Appl. Math., 22 (1993), 123-138
  • Lesław Gajek, D. Zagrodny, A new approach to sufficient conditions for Pareto optimality, Preprint, Tech. Univ. Łódź, (1993),
  • Lesław Gajek, D. Zagrodny, Fixed point theorems related to a general multiobjective optimization problem, Scientific Bulletin of Łódź Technical University, Volume dedicated to Professor W. Krysicki on his 88 th birthday, 25 (1993), 51-69
  • Lesław Gajek, Marek Kałuszka, Upper bounds for the L1-risk of the minimum L1-distance regression estimator, Annals of the Institute of Statistical Mathematics, 44 (1992), 737-744, JCR
  • Lesław Gajek, D. Zagrodny, Countably orderable sets and their applications in optimization, Optimization, 26 (1992), 287-301, JCR
  • Lesław Gajek, Minimum L1 -penalized distance estimators of a density and its derivatives, Probab. Math. Statist., 13 (1992), 245-252
  • Lesław Gajek, The rate of strong consistency of a class of nonparametric hazard function estimators, Sankhya, Ser. A, 54 (1992), 97-106, JCR
  • Lesław Gajek, D. Zagrodny, Existence of maximal points with respect to ordered bipreference relations, Journal of Optimization Theory and Applications, 70 (1991), 355-364, JCR
  • Lesław Gajek, U. Gather, Moment inequalities for order statistics with applications to characterizations of distributions, Metrika, 38 (1991), 357-367, JCR
  • Lesław Gajek, U. Gather, Estimating a scale parameter under censorship, Statistics, 22 (1991), 529-549, JCR
  • L. D. Brown, Lesław Gajek, Information inequalities for the Bayes risk, Ann. Statist., 18 (1990), 1578-1594, JCR
  • Lesław Gajek, U. Gather, Characterizations of the exponential distribution by failure rate and moment properties of order statistics, Extreme value theory,(Oberwolfach 1987), Lecture Notes in Statistics, Springer, 51 (1989), 114-124
  • Lesław Gajek, Estimating a density and its derivatives via the minimum distance method, Probab. Th. Rel. Fields, 80 (1989), 601-617, JCR
  • Lesław Gajek, On the minimax value in the scale model with truncated data, Ann. Statist., 16 (1988), 669-677, JCR
  • Lesław Gajek, Minimum penalized distance estimation of a density and its derivatives (in Polish), Rozprawa habilitacyjna Nr 103, Scient. Bull. PŁ, 533 (1988),
  • Lesław Gajek, An improper Cramer-Rao lower bound, Appl. Math., XIX (1987), 73-87
  • Lesław Gajek, Generalized Bayes estimators of a non-linear function of the natural parameter of an exponential family of distributions, Demonstratio Math., XX (1987), 355-365
  • Lesław Gajek, On improving distribution function estimators which are not monotonic functions, Statist. Probab. Letters, 5 (1987), 213-215, JCR
  • Lesław Gajek, On improving density estimators which are not bona fide functions, Ann. Statist., 14 (1986), 1612-618, JCR
  • Lesław Gajek, On some characteristic properties of the Koopman-Darmois family of distributions, Demonstratio Math., XIX (1986), 197-202
  • Lesław Gajek, A remark on Lehmann-unbiased estimators for scale resp. location parameters, Metrika, 32 (1985), 73-84, JCR
  • Lesław Gajek, Limiting properties of the difference between the successive k-th record values, Probab. Math. Statist., 5 (1985), 221-224
  • Lesław Gajek, Sufficient conditions for admissibility, Proc. 4 Pann. Symp. Math. Statist., Bad Tatzmannsdorf, Reidel-Akademiai Kiado, (1983), 107-116
  • Lesław Gajek, A characterization and some properties of generalized gamma distributions, Scient. Bull. PŁ, Ser. Mat., 15 (1982), 149-164
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