Books:

G.Larcher: The Art of Quantitative Finance Vol. 1, Trading, Derivatives and Basic Concepts. Springer Verlag, 2023. 

G. Larcher: The Art of Quantitative Finance Vol. 2, Volatilities, Stochastic Analysis and Valuation Tools. Springer Verlag, 2023.

G.Larcher: The Art of Quantitatives Finance Vol. 3, Risk, Optimal Portfolios, and Case Studies. Springer Verlag, 2023. 

G. Larcher: Die Black-Scholes-Theorie: In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis. Springer-Gabler-Verlag, 2022.

G. Larcher: Quantitative Finance: Strategien, Investments, Analysen. Springer-Gabler-Verlag, 2020.

G. Larcher, F. Pillichshammer, A. Winterhof, Ch. Xing. Applied Algebra and Number Theory, Cambridge University Press, Cambridge, ISBN 9781107074002. 2014.

Publications:

R. Hofer, G. Larcher: The exact order of discrepancy for Levin’s normal number in base 2. To appear in: Journal de Théorie des Nombres des Bordeaux, 2023.

Hofer, R. and Larcher, G.: Discrepancy bounds for normal numbers generated by necklaces in arbitrary base. Journal of Complexity, Vol. 78, pp. 101767, 2023.

A. Brunhuemer, L. Larcher, P. Seidl,  S. Desmettre, J. Kofler, G. Larcher:  Supervised Machine Learning Classification for Short Straddles on the S&P500. In: Risks, 10(12), 235, 25 Seiten, 2022.

A. Brunhuemer, G. Larcher: Quasi-Monte Carlo methods in portfolio selection with many constraints. In: Botev, Z., et al. (eds.), Advances in Modeling and Simulation, 89-109, Springer, Cham, 2022.

A. Brunhuemer, G. Larcher, L. Larcher: Analysis of Option Trading Strategies Based on the Relation of Implied and Realized S&P500 Volatilities. ACRN Journal of Finance and Risk Perspective, Vol. 10, Special Issue 18th FRAP Conference, pp. 166-203, 2021.

L. Kaltenböck, G. Larcher: On Bounded Remainder Intervals and Strongly Non-Bounded Remainder Intervals for Sequences ({a_n α})_{n≥1}. Journal of Number Theory, Vol. 199, pp. 126 - 149, 2019.

A. Hinrichs, L. Kaltenböck, G. Larcher, W. Stockinger, M. Ullrich: On a multi-dimensional Poissonian pair correlation concept and uniform distribution. Monatshefte Mathematik, Vol. 190, Nr. 2 pp. 333-352, 2019.

G. Larcher, W. Stockinger: Pair correlation of sequences ({a_n α})_nεN with maximal additive energy. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 168, pp. 287-293, 2020.

G. Larcher, W. Stockinger: Some negative results related to Poissonian pair correlation problems. Discrete Mathematics, Vol. 343, Nr. 2, pp. 18, 2020.

I. Aichinger, C. Aistleitner, G. Larcher. On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics. Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan (J. Dick, F. Y. Kuo, H. Wozniakowski, eds.), Springer-Verlag, pp. 1-16, 2018.

M. Drmota, R. Hofer, G. Larcher. On the discrepancy of Halton-Kronecker sequences. To appear in: Number Theory - Diophantine problems, Uniform Distribution and Applications - Festschrift in Honour of Robert F. Tichy's 60th Birthday (editors Christian Elsholtz and Peter Grabner). 2017.

C. Aistleitner, G. Larcher, M. Lewko. Additive energy and the Hausdorff Dimension of the Exceptional Set in metric Pair Correlation Problems. With an Appendix by Jean Bourgain. Israel Journal of Mathematics, Vol. 222, Nr. 1, pp. 463-485, 2017.

S. Grepstad, G. Larcher. On pair correlation and discrepancy. Arch. Math. (109), pp. 143-149, 2017.

I. Aichinger, G. Larcher. Sets of Bounded Remainder for the Billiard on a Square. Uniform Distribution Theory, Vol. 13, Nr. 2, pp. 71-82, 2019.

C. Aistleitner, G. Larcher, F. Pillichshammer, S. Saad-Eddin, R. Tichy. On Weyl Products and Uniform Distribution Modulo One. Monatsh. Math. Vol. 185, Nr. 3, pp. 365-395, 2018.

A. Hinrichs, G. Larcher. An improved lower bound for the L_2-discrepancy. Journal of Complexity, Vol 34, pp. 68-77, 2016.

G. Larcher. On the discrepancy of sequences in the unit interval. Indagationes Math., Vol 27, Nr. 2, pp. 546-558, 2016.

C. Aistleitner, R. Hofer, G. Larcher. On Evil Kronecker Sequences and Lacunary Trigonometric Products. Annales de´l Institute Fourier, Vol 67, Nr. 2, pp. 637-687, 2017.

C. Aistleitner, G. Larcher. Metric results on the discrepancy of sequences (a_n α)_n ≥ 1 modulo one for integer sequences (a_n)_n ≥ 1 with polynomial growth behavior. Mathematika, Vol 62, pp. 478-491. 2016.

C. Aistleitner, G. Larcher. On sequences with prescribed metric discrepancy behavior. Monatsh. Math., Vol. 181, pp. 507-514, 2016.

C. Aistleitner, G. Larcher. Additive Energy and Irregularities of Distribution. Uniform Distribution Theory, Vol. 12, Nr. 1, pp. 99-107, 2017.

S. Grepstad, G. Larcher. Sets of bounded remainder fo the continuous irrational rotation on [0,1)^2. Acta Arithmetica, pp. 365-395, 2016.

C. Aistleitner, R. Hofer, G. Larcher. Some recent developments at the intersection of Diophantine approximation, analytic number theory, and irregularities of distribution. RIMS Kokyoroku, pp. 161-172, 2017.

G. Larcher. On the star-discrepancy of sequences in the unit-interval. J. Complexity (31), pp. 474-485, 2015.

G. Larcher, F. Puchhammer. An improved bound for the star discrepancy of sequences in the unit interval. Uniform Distribution Theory (10), Nr. 2, pp. 1-14, 2015.

G. Larcher, W. Ch. Schmid. Harald Niederreiter at 70. Unifrom Distribution Theory (10). Nr. 1, pp. i-v, 2015.

M. Drmota, P. Grabner, P. Hellekalek, R. Hofer, P. Kritzer, G. Larcher, G. Leobacher, F. Pillichshammer, R. Tichy, A. Winterhof. The FWF-Special Research Area "Quasi-Monte Carlo Methods: Theory and Applications", in: Internat. Math. Nachrichten, Vol 226, pp. 1-19, 2014.

P. Kritzer, G. Larcher, F. Pillichshammer. Discrepancy estimates for index-transformed uniformly distributed sequences. Funct. Approx. Comment. Math. (51), pp. 197-220, 2014.

G. Larcher, F. Pillichshammer. A metrical lower bound on the star discrepancy of digital sequences. Monatsh. Math. (174), pp. 105-123, 2014.

G. Larcher, F. Pillichshammer. Metrical lower bounds on the discrepancy of digital Kronecker-sequences. J. Number Theory (135), pp. 262-283, 2014.

G. Larcher. Discrepancy estimates for sequences: new results and open problems. Uniform distribution and quasi-Monte Carlo methods - Discrepancy, integratoin and applications, pp. 171-190, de Gruyter, Berlin. 2014.

G. Larcher. Quantitive Rearrangement Theorems for Sequences in Compact Spaces. Uniform Distribution Theory (9), Nr. 1, pp. 79-98, 2014.

L. Del Chicca, G. Larcher. Hybrid Monte Carlo-Methods in Credit Risk Managment. Monte Carlo Methods and Applications (Bd. 20), Nr. 4, pp. 245-260, 2014.

G. Larcher, F. Pillichshammer, A. Winterhof, Ch. Xing. Some highlights of Harald Niederreiter´s work. In: Applied Algebra and Number Theory, pp. 1-21, Cambridge University Press, Cambridge. 2014.

P. Kritzer, G. Larcher. On the Arrangement of Point Sets in the Unit Interval. Manuscripta Mathematica (140), pp. 377-391, 2013.

L. Del Chicca, G. Larcher, M. Szölgyenyi. Modeling and Performance of Certain Put-Write-Strategies. The Journal of Alternative Investments (15), Nr. 4, pp. 74-86, 2013.

G. Larcher. Probabilistic Diophantine Approximation and the Distribution of Halton-Kronecker Sequences. J. Complexity (29), pp. 397-423, 2013.

R. Hofer, G. Larcher. Metrical Results on the Discrepancy of Halton-Kronecker-Sequences. Mathematische Zeitschrift (271), pp. 1-11, 2012.

R. Hofer, G. Larcher, H. Zellinger. On the Digits of Squares and the Distribution of Quadratic Subsequences of Digital Sequences. Proceedings of the AMS (141), Nr. 5, pp. 1551-1565, 2012.

L. Del Chicca, G. Larcher. Portfolio-Selektion unter Berücksichtigung von Nachhaltigkeitsparametern. Ethical Finance, Finance & Science Reihe (Bd. 1), pp. 343-357, Hg: J. Krall et al., Peter Lang Verlag. 2012.

L. Del Chicca, G. Larcher. A Comparison of Different Families of Put-Write Option Strategies. ACRN Journal of Finance and Risk Perspectives (1), Nr. 1, pp. 1-14, 2012.

J. Dick, G. Larcher, F. Pillichshammer, H. Wozniakowski. Exponential Convergence and Tractability of Multivariate Integration for Korobov Spaces. Math. Comp. (80), pp. 905-930, 2011.

G. Larcher, H. Zellinger. On Irregularities of Distribution of Weighted Sums-of-Digits. Discrete Mathematics (311), pp. 109-123, 2011.

L. Del Chicca, G. Larcher. On the Individual Expectations of Non-Average Investors. Journal of Mathematical Finance (1), Nr. 3, pp. 72-82, 2011.

R. Hofer, G. Larcher. On Existence and Discrepancy of Certain Digital Niederreiter-Halton Sequences. Acta Arithmetica (141), Nr. 4, pp. 369-394, 2010.

R. Hofer, P. Kritzer, G. Larcher, F. Pillichshammer. Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Int. J. Number Theory (5), Nr. 4, pp. 719-746, 2009.

G. Larcher, F. Pillichshammer. The sum of distances between vertices of a convex polygon with unit perimeter. Amer. Math. Monthly (115), pp. 350-355, 2008.

R. Hofer, G. Larcher, F. Pillichshammer. Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Monatsh. Math. (154), Nr. 3, pp. 199-230, 2008.

L. Del Chicca, G. Larcher. Der Preis des Risikos: Optionen und Erwartungen. Schriftenreihe der Finance&Ethics Academy (Band 2), pp. 50-72, K.-H. Brodbeck (Hg.). 2008.

G. Larcher, F. Pillichshammer. A note on optimal point distributions in [0,1)^s. J. Comput. Appl. Math. (206), pp. 977-985, 2007.

P. Kritzer, G. Larcher, F. Pillichshammer. A through analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Ann. Mat. Pura Appl. (189), Nr. 2, pp. 229-250, 2007.

G. Larcher, F. Pillichshammer. An extremum problem for convex polygons. Anz. Österreich. Akad. Wiss. Math-Natur. Kl. (215), pp. 173-176, 2006.

G. Larcher, F. Pillichshammer. Moments of the weighted sum-of-digits function. Quaestiones Mathematicae (28), Nr. 3, pp. 321-336, 2005.

M. Drmota, G. Larcher, F. Pillichshammer. Precise distribution properties of the van der Corput sequence and related sequences. Manuscripta Math. (118), pp. 11-41, 2005.

G. Larcher, G. Leobacher. Quasi-Monte Carlo and Monte Carlo methods and their applications in finance. Surveys on Mathematics for Industry (11), pp. 95-130, 2005.

G. Larcher, F. Pillichshammer. Remarks on the weighted sum-of-digits function. books@ocg. at (189), pp. 27-35, 2005.

G. Larcher, F. Pillichshammer. Walsh series analysis of the star discrepancy of digital nets and sequences. Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 315-328, 2004.

G. Larcher, G. Leobacher. An optimal strategy for hedging with short-term futures contracts. Mathematical Finance (13), Nr. 2, pp. 331-344, 2003.

G. Larcher, M. Predota, R. Tichy. Arithmetic average options in the hypberbolic model. Monte Carlo Methods and Appl. (9), Nr. 3, pp. 227-239, 2003.

G. Larcher, G. Leobacher, K. Scheicher. On the tractability of the Brownian Bridge algorithm. Journal of Complexity (19), pp. 511-528, 2003.

G. Larcher, F. Pillichshammer. Sums of distances to the nearest integer and the discrepancy of digital nets. Acta Arith. (106), pp. 379-408, 2003.

G. Larcher, F. Pillichshammer, K. Scheicher. Weighted Discrepancy and High-Dimensional Numerical Integration. BIT Numerical Mathematics (43), Nr. 1, pp. 123-137, 2003.

G. Larcher, F. Pillichshammer. On the L_2-discrepancy of the Sobol-Hammersley net in dimension 3. J. Complexity (18), pp. 415-448, 2002.

M. Drmota, G. Larcher. The Sum-of-Digits-Function and Uniform Distribution Modulo 1. Journal of Number Theory (89), pp. 65-96, 2001.

G. Larcher, F. Pillichshammer. Walsh series analysis of the L_2-discrepancy of symmetrisized point sets. Monatsh. Math. (132), pp. 1-18, 2001.

G. Larcher, W.Ch. Schmid, R. Wolf. On the approximation of certain mass distributions appearing in distance geometry. Acta Math. Hung. (87), Nr. 4, pp. 295-316, 2000.

G. Larcher, I. Pirsic. Base change problems for generalized (W)alsh series, digital derivatives, and multivariate numerical integration. Pacific Journal of Mathematics (189), pp. 75-105, 1999.

J. Eichenauer-Herrmann, G. Larcher, R. Wolf. On the average discrepancy of successive tuples of pseudorandom numbers over parts of the period. Monatsh. Math. (127), pp. 141-154, 1999.

G. Larcher. A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators. Acta Arith. (83), pp. 1-15, 1998.

G. Larcher. Digital Point Sets: Analyis and Applications. Springer Lecture Notes in Statistics (138), pp. 167-222, 1998.

P. Hellekalek, G. Larcher. Random- and Quasi Random Point Sets. Springer Lecture Notes in Statistics, Springer, New York, 1998.

J. Eichenauer-Herrmann, F. Emmerich, G. Larcher. Average discrepancy, hyperplanes, and compound pseudorandom numbers. Finite Fields Appl. (3), Nr. 3, pp. 203-218, 1997.

J. Eichenauer-Herrmann, G. Larcher. Average equidistribution properties of compound nonlinear congruential pseudorandom numbers. Math. Comp. (66), pp. 363-372, 1997.

G. Larcher. Metric results on the approximation of zero by linear combinations of independent and of dependent rationals. Manuscripta Math. (94), pp. 501-529, 1997.

G. Larcher. On the distribution of digital sequences. Springer Lecture Notes in Statitstics (127), pp. 109-123, 1997.

G. Larcher, I. Pirsic, R. Wolf. Quasi-Monte Carlo integration of digitally smooth funcions by digital nets. Springer Lecture Notes in Statistics (127), pp. 321-329, 1997.

J. Eichenauer-Herrmann, G. Larcher. Average behaviour of compound nonlinear congruential pseudorandom numbers. Finite Fields Appl. (2), pp. 111-123, 1996.

G. Larcher, H. Niederreiter, W. Ch. Schmid. Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration. Monatsh. Math. (121), pp. 231-253, 1996.

G. Larcher, R. Wolf. Nets constructed over finite fields and the numerical integration of multivariative Walsh series. Finite Fields Appl. (2), pp. 304-320, 1996.

G. Larcher. On the number of odd binomial coefficients. Acta Math. Hungarica (71), Nr. 3, pp. 177-197, 1996.

G. Larcher, A. Lauß, H. Niederreiter, W.Ch. Schmid. Optimal polynomials for (t,m,s)-nets and numerical integration of multivariate Walsh series. SIAM J. Numer. Analysis (33), Nr. 6, pp. 2239-2253, 1996.

G. Larcher, W.Ch. Schmid, R. Wolf. Quasi-Monte Carlo methods for the numerical integration of multivariate Walsh series. Math. Comput. Modelling (23), Nr. 8-9, pp. 55-67, 1996.

D. Brunner, G. Larcher, W.Ch. Schmid. PANUMIWAL: a system for the parallel numerical integration of high-dimensional functions. Proc. International Workshop "Parallel Numerics '96", (Godz Martuljek). 1996.

C. Biester, P. Grabner, G. Larcher, R. Tichy. Adaptive search in quasi-Monte Carlo optimization. Math. Comp. (64), pp. 807-818, 1995.

G. Larcher, H. Niederreiter. Generalized (t,s)-sequences, Kronecker-type sequences, and diophantine approximations of formal Laurent series. Trans. Amer. Math. Soc. (347), pp. 2051-2073, 1995.

G. Larcher. On the distribution of an analog to classical Kronecker-sequences. J. Number Theory (52), pp. 198-215, 1995.

G. Larcher, W. Ch. Schmid. On the numerical integration of high-dimensional Walsh series by quasi-Monte Carlo methods. Math. Comput. Simulation (38), pp. 127-134, 1995.

G. Larcher, W. Ch. Schmid, R. Wolf. Digital (t,m,s)-nets, digital (t,s)-sequences, and numerical integration of multivariate Walsh series. Proc. Salzburg Symposium on Pseudorandom Number Generation and Quasi-Monte Carlo methods, ACPC Technical Report (95), Nr. 4, pp. 75-107, 1995.

G. Larcher, A. Lauß, W. Ch. Schmid. Classical number-theoretical integration methods and the Walsh series lattice rule: a comparison. Proc. International Workshop "Parallel Numerics '95" (Sorrent), pp. 47-66, 1995.

G. Larcher, W. Ch. Schmid. Multivariate Walsh series, digital nets and Quasi-Monte Carlo integration. Springer Lecture Notes in Statistics (106), pp. 252-262, 1995.

G. Larcher. On the numerical integration of Walsh series by number-theoretic methods. Math. Comp. (63), pp. 277-291, 1994.

G. Larcher, C. Traunfellner. On the numerical integration of Walsh series by number-theoretic methods. Math. Comp. (63), pp. 277-291, 1994.

G. Larcher. On the two-dimensional Kronecker-sequence and a class of ergodic skew-products. Arch. Math. (63), pp. 231-237, 1994.

G. Larcher, W. Ch. Schmid, R. Wolf. Representation of functions as Walsh series to different bases and an application to the numerical integration of high-dimensional Walsh series. Math. Comp. (63), pp. 701-716, 1994.

G. Larcher, W. Ch. Schmid. Representation of functions as Walsh series to different bases and an application to the numerical integration of high-dimensional Walsh series. Math. Comp. (63), pp. 701-716, 1994.

G. Larcher, W. Ch. Schmid. Numerical integration of multivariate Walsh series by means of different (t,m,s)-nets. Proc. International Workshop "Parallel Numerics '94" (Smolenice, Slow.), pp. 24-43, 1994.

G. Larcher. Quantitive rearrangement theorems for sequences in compact spaces. Arbeitsberichte, Institut für Mathematik, Universität Salzburg (2/94), pp. 1-22, 1994.

G. Larcher, H. Niederreiter. Kronecker-type sequences and nonarchimedean diophantine approximations. Acta Arith. (63), pp. 379-396, 1993.

G. Larcher. Nets obtained from rational functions over finite fields. Acta Arith. (63), pp. 1-13, 1993.

G. Larcher. Zur Diskrepanz verallgemeinerter Ziffernsummenfolgen. Sitzungsber. Österr. Akad. Wiss. Math. - Naturw. Kl. II (202), pp. 179-185, 1993.

G. Larcher, H. Niederreiter. A lower bound for the dispersion of multi-dimensional sequences. K. Nagasaka, editor, Analytic Number Theory and related topics. World Scientific Publishing, pp. 81-86, 1993.

G. Larcher. A class of low-discrepancy point sets and its application to numerical integration by number-theoretical methods. Grazer Math. Berichte (318), pp. 69-80, 1993.

G. Larcher. Bemerkung zur Diskrepanz einer Klasse von Folgen. Anz. Österr. Akad. Wiss., pp. 1-4, 1991.

G. Larcher. Corrigendum to the paper: On the distribution of s-dimensional Kronecker-sequences. Acta Arith. (60), pp. 93-95, 1991.

G. Larcher. On the cube-discrepancy of Kronecker-sequences. Arch. Math. (Basel) (57), pp. 362-369, 1991.

G. Larcher. An inequality with applications in diophantine approximation. Springer Lecture Notes in Mathematics (1452), pp. 132-138, 1990.

P. Hellekalek, G. Larcher. On Weyl Sums and skew-products over irrational rotations. Theoret. Comput. Sci. (65), pp. 189-196, 1989.

P. Hellekalek, G. Larcher. On functions with bounded remainder. Annales de l'institut Fourier (39), pp. 17-26, 1989.

G. Larcher. On the distribution of the multiples of an s-tube of real numbers. J. Number Theory (31), pp. 367-372, 1989.

G. Larcher, H. Niederreiter. Optimal coefficients modulo prime powers in the three-dimensional case. Ann. Mat. Pura Appl. (155), pp. 299-315, 1989.

G. Larcher, R. Tichy. Some number-theoretical properties of generalized sum-of-digit functions. Acta Arith. (52), pp. 183-196, 1989.

G. Larcher. A convergence problem connected with continued fractions. Proc. Amer. Math. Soc. (103), pp. 718-722, 1988.

G. Larcher. A new extremal property of the Fibonacci ratio. Fibonacci Quart. (26), pp. 247-255, 1988.

G. Larcher, R. Tichy. Arithmetical properties of the Standard Gray-Code. Sitzungsber. Österr. Akad. Wiss. Math. - Naturw. Kl. II (197), pp. 449-461, 1988.

G. Larcher. On the distribution of s-dimensional Kronecker-sequences. Acta Arith. (51), pp. 335-347, 1988.

G. Larcher. On the distribution of sequences connected with digit representation. Manuscripta Math. (61), pp. 33-42, 1988.

G. Larcher. A best lower bound for good lattice points. Monatsh. Math. (104), pp. 45-51, 1987.

G. Larcher, R. Tichy. A note on Gray code and odd-even merge. Discrete Appl. Math. (18), pp. 309-313, 1987.

G. Larcher, R. Tichy, N. Kopecek, G. Turnwald. On the discrepancy of sequences associated with the sum of digits function. Annales de'Institut Fourir (37), Nr. 3, pp. 1-17, 1987.

G. Larcher. Exponential sums of digit-depending sequences. Arbeitsberichte, Institut für Mathematik, Universität Salzburg (1/87), pp. 1-25, 1987.

G. Larcher. On the distribution of sequences connected with good lattice points. Monatsh. Math. (101), pp. 135-150, 1986.

P. Hellekalek, G. Larcher. On the ergodicity of a class of skew-products. Israel J. Math. (54), pp. 301-306, 1986.

G. Larcher. Quantitive rearrangement theorems. Compositio Math. (60), pp. 251-259, 1986.

G. Larcher. The dispersion of a special sequence. Arch. Math. (Basel) (47), pp. 347-352, 1986.

G. Larcher. Über die isotrope Diskrepanz von Folgen. Arch. Math. (Basel) (46), pp. 240-249, 1986.

G. Larcher. Optimale Koeffizienten bezüglich zusammengesetzter Zahlen. Monatsh. Math. (100), pp. 127-135, 1985.

G. Larcher. Optimale Koeffizienten bezüglich zusammengesetzter Zahlen. Arbeitsberichte, Institut Mathematik, Universität Salzburg (4/84), pp. 87-157, 1984.

G. Larcher. Numerische analytische Fortsetzung von Funktionen. Arbeitsberichte Universität Salzburg (4/82), pp. 1-44, Diplomarbeit. 1982.