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College of Arts & Sciences

Archil Gulisashvili

Archil Gulisashvili

Professor

Mathematics
555 Morton Hall
gulisash@ohio.edu
740-593-1281

Education

Dr.Sc., Tbilisi State University

Research Interests

Analysis

  • Classical and applied harmonic analysis

Publications

Books

Large Deviations and Asymptotic Methods in Finance, Springer Proceedings in
Mathematics and Statistics, Vol 110, P. K. Friz, J. Gatheral, A. Gulisashvili, A.
Jacquier, J. Teichmann (Eds.), Springer International Publishing Switzerland, 2015.

A Gulisashvili, Analytically Tractable Stochastic Stock Price Models, Springer Fi-
nance, 2012.

A. Gulisashvili and J. A. van Casteren, Non-Autonomous Kato Classes and Feynman-
Kac Propagators, World Scientific, Singapore, 2006.

Book Chapters

(With P. Tankov), Implied volatility of basket options at extreme strikes, in: Large
Deviations and Asymptotic Methods in Finance, Springer Proceedings in Mathe-
matics and Statistics, Vol 110, P. K. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier,
J. Teichmann (Eds.), Springer International Publishing Switzerland, 2015, pp. 175-
212.

(With J. Teichmann), The Gärtner-Ellis theorem, homogenization, and affine pro-
cesses, in: Large Deviations and Asymptotic Methods in Finance, Springer Pro-
ceedings in Mathematics and Statistics, Vol 110, P. K. Friz, J. Gatheral, A. Gulisas-
hvili, A. Jacquier, J. Teichmann (Eds.), Springer International Publishing Switzer-
land, 2015, pp. 287-320.

(With J. Vives), Asymptotic behavior of the distribution densities in models with
jumps, in: M. Zili and D. V. Filatova (eds.), Stochastic Differential Equations and Pro-
cesses, Springer Proceedings in Mathematics, 7
, Springer-Verlag, Berlin Heidelberg,
2011, 237-252.

Free propagators and Feynman-Kac propagators, Seminar of Mathematical Analy-
sis, Proceedings, Universities of Malaga and Seville (Spain), September 2003-June
2004, Daniel Girela Alvarez, Genaro Lopez Acedo, Rafael Villa Carro, eds., Uni-
versidad de Sevilla, 2004, 47-64.

Nonautonomous Kato classes and the behavior of backward Feynman-Kac prop-
agators, Analyse stochastique et theorie du potentiel, Saint Priest de Gimel (2002),
Association Laplace-Gauss, 2003, 5 pages.

On the Kato classes of distributions and the BMO-classes, in “Differential Equa-
tions and Control Theory” (eds. S. Aizikovici and N. Pavel), Lecture Notes in Pure
and Applied Mathematics, v. 225, Marcel Dekker, Inc., New York, 2001, 159-176.

(With G. Muraz) Rearrangement-invariant hulls and kernels of the amalgam spaces
on Rn, in “Function Spaces” (Hudzik/Skrzypczak, eds), Marcel Dekker, Inc., 2000,
171-180.

Hulls and kernels of function classes on Rn, in “Recent Developments in Complex
Analysis and Computer Algebras” (J. Gilbert, J. Kajiwara, and Y. Xu, eds.) Kluwer,
Dordrecht, 1999, 81-94.

Rearrangement-invariant hulls of sets, Linear and Complex Analysis, Problem Book,
Lecture Notes in Math., 1043, (1984), 642-645.

Estimates for the Pettis integral in interpolation spaces with some applications,
Banach Space Theory and its Applications, Proceedings, Bucharest, 1981, Lecture Notes
in Math, 991 (1983), 55-76.

Submitted Papers and Working Papers

Gaussian stochastic volatility models: Scaling regimes, large deviations, and mo-
ment explosions, submitted for publication, 2018, available on arXiv:1808.00421

(with Ch. Bayer, P. K. Friz, B. Horvath, and B. Stemper) Short-time near-the-money
skew in rough fractional volatility models, accepted for publication in Quantita-
tive Finance (2018); available on arXiv:1703.05132

(with P. K. Friz, B. Horvath, and P. Pigato), A unified approach to asymptotics of
exotic digitals, working paper, 2017.

(with M. Lagunas, R. Merino, and J. Vives), Higher order approximation of plain
vanilla option prices under stochastic volatility models, working paper, 2017.

Beyond the Gärtner-Ellis theorem with applications to time-averages of the Ornstein-
Uhlenbeck process, working paper, 2016.

Published Papers

Large deviation principle for Volterra type fractional stochastic volatility models,
SIAM Journal on Financial Mathematics, 9 (2018), 1102-1136; available on arXiv:1710.10711

(with F. Viens and X. Zhang) Small-time asymptotics for Gaussian self-similar sto-
chastic volatility models, Applied Mathematics and Optimization (2018).
https://doi.org/10.1007/s00245-018-9497-6, 41 p., available on arXiv:1505.05256,
2016.

(with F. Viens and X. Zhang) Extreme-strike asymptotics for general Gaussian sto-
chastic volatility models, Annals of Finance (2018). https://doi.org/10.1007/s10436-
018-0338-z, 43 p., available on arXiv:1502.05442v3, 2017.

(with B. Horvath and A. Jacquier) Mass at zero in the uncorrelated SABR model
and implied volatility asymptotics, Quantitative Finance, 18 (2018), 1753-1765;
available on arXiv:1502.03254

Distance to the line in the Heston model, Journal of Mathematical Analysis and
Applications, 450 (2017), 197-228; available on arXiv:1409.6027.

(With P. K. Friz, B. Gess, and S. Riedel), The Jain-Monrad criterion for rough paths
and applications to Random Fourier Series and Non-Markovian Hörmander The-
ory, Annals of Probability, 44 (2016) 684-738.

(With P. Tankov) Tail behavior of sums and differences of log-normal random vari-
ables, Bernoulli, Volume 22, Number 1 (February 2016), 444-493.

(with B. Horvath and A. Jacquier), On the probability of hitting the boundary for
Brownian motions on the SABR plane, Electronic Communications in Probability,
21, No 75 (2016), 1-13.

(with J. Vives) Asymptotic analysis of stock price densities and implied volatilities
in stochastic volatility models with Lévy type jumps, SIAM Journal on Financial
Mathematics 6 (2015), pp. 158-188.

Left-wing asymptotics of the implied volatility in the presence of atoms, Interna-
tional Journal of Theoretical and Applied Finance, 18, 1550013 (2015) [25 pages].

(With P. Laurence), The Heston Riemannian distance function, Journal de mathématiques
pures et appliquées,
101, (2014) 303-329.

Asymptotic equivalence in Lee’s moment formulas for the implied volatility, as-
set price models with moment explosions, and Piterbarg’s conjecture, International
Journal of Theoretical and Applied Finance
, 15, (2012) 1250020 (34 pages).

(With P. K. Friz, S. Gerhold, and S. Sturm), On refined volatility smile expansion in
the Heston model, Quantitative Finance, 11, (2011) 1151-1164.

(With E. M. Stein) Asymptotic behavior of the distribution densities in models with
stochastic volatility, I , Mathematical Finance, 20 (2010), 447-477.

(With E. M. Stein) Asymptotic behavior of the stock price distribution density and
implied volatility in stochastic volatility models, Applied Mathematics and Optimiza-
tion
, 61, (2010), 287-315.

Asymptotic formulas with error estimates for call pricing functions and the im-
plied volatility at extreme strikes, SIAM Journal on Financial Mathematics, 1, (2010)
609-641.

(With E. M. Stein) Implied volatility in the Hull-White model, Mathematical Finance,
19 (2009), 303-327.54. Markov processes, classes of time-dependent measures, and
Feynman-Kac propagators, Transactions of the American Mathematical Society, 360
(2008), 4063-4098.

Markov processes, classes of time-dependent measures, and Feynman-Kac propa-
gators, Transactions of the American Mathematical Society, 360 (2008), 4063-4098.

(With E. M. Stein) Asymptotic behavior of the distribution of the stock price in
models with stochastic volatility: The Hull-White model, Comptes Rendus Acad Sci.
Paris
, 343 (2006), 519-523.

Nonautonomous Kato classes of measures and Feynman-Kac propagators, Trans-
actions of the American Mathematical Society
, 357 (2005), 4607-4632.

Feynman-Kac propagators and viscosity solutions (with J. van Casteren), Journal
of Evolution Equations
5 (2005), 105-121.

On the heat equation with a time-dependent singular potential, Journal of Func-
tional Analysis
, 194, No 1 (2002).

Classes of time-dependent measures and the behavior of Feynman-Kac propaga-
tors, C. R. Acad. Sci. Paris, Ser. I 334 (2002), 445-449.

(With M. Cwikel) Interpolation on families of characteristic functions, Studia Math-
ematica
, 138 (2000), 209-224.

Sharp estimates in smoothing theorems for Schrödinger semigroups, Journal of
Functional Analysis
, 170 (2000), 161-187.

Rearrangements of functions on a locally compact abelian group and integrability
of the Fourier transform, Journal of Functional Analysis, 146, No 1 (1997), 62-115.

Rearrangement-invariant spaces of functions on LCA groups, Journal of Functional
Analysis
, 156 (1998), 384-410.

(with M. Kon) Exact smoothing properties of Schrödinger semigroups, American
Journal of Mathematics, 118, No 6 (1996), 1215-1248.

(with C.R. MacCluer) Linear chaos in the quantum harmonic oscillator, American
Society of Mechanical Engineering, Journal of Dynamic Systems, Measurement, and Con-
trol
, 118, June 1996, 337-338.

(with R. Merletti and L.R. Lo Conte) Estimation of shape characteristics of surface
EMG spectra from time domain data, IEEE Transactions in Biomedical Engineering, 42, No 8 (1995), 769-776.

(with G. Sandri) Quasianalytic function classes and the complex-time diffusion
group, Mathematical Models and Methods in Applied Sciences, 5, No 2 (1995), 167-190.

On the Dimensionality Problem for Classes of Band-Limited Functions, in “The In-
teraction Between Functional Analysis, Harmonic Analysis, and Probability”, The
Department of Mathematics, University of Missouri at Columbia, 1994, p. 8 – ab-
stract.

(with M. Kon) Smoothness of Schrödinger semigroups and eigenfunctions, Inter-
national Mathematics Research Notices
, No 5 (1994), 193-199.

Mean dimension of function classes with Lebesgue measurable spectral sets, Jour-
nal of Approximation Theory
, 75, No.1 (1993), 44-78.

A capacitary weak type estimate for spherical maximal functions, Abstracts of the
AMS
, 13, No. 2 (1992), 291.

Mean ε-dimension of classes of functions with spectra in a given set, Doklady of the
USSR Academy of Sciences
, 317, No.4 (1991), 803-807 (in Russian).

On the trace and extension operators for Besov spaces, Proceedings of the Tbilisi In-
stitute of Mathematics
, 95 (1989), 39-55 (in Russian).

Traces of functions belonging to Sobolev and Besov spaces and extensions from
subsets of Euclidean space, Zapiski Nauchnyh Seminarov LOMI (Leningrad Inst. of
Math.)
, 157 (1987), 137-145 (in Russian). English translation in the Journal of Soviet
Mathematics
, 44, No.6 (1989).

Traces of differentiable functions on subsets of Euclidean space, Zapiski Nauchnyh
Seminarov LOMI (Leningrad Inst. of Math.)
, 149 (1986), 52-66 (in Russian). English
translation in the Journal of Soviet Math., 42, No.2 (1988), 1573-1583.

On traces of Besov spaces and the convergence of singular integrals, Reports of the
Vekua Institute of Applied Mathematics Seminars
(Tbilisi), 3, No.2 (1988), 33-36 (in
Russian).

On the traces of differentiable functions on subsets of Euclidean space, Leningrad
Inst. of Math.
Preprint No 2-85, Leningrad (1985) (in Russian).

Multipliers in Besov spaces, Zapiski Nauchnyh Seminarov LOMI (Leningrad Institute
of Mathematics)
, 135 (1984), 36-50 (in Russian). English translation in the Journal of
Soviet Mathematics,
31, No.1 (1985).

Multipliers in Besov spaces and traces of functions on subsets of Euclidean space,
Doklady of the USSR Academy of Sciences, 287, No.4 (1985), 777-781 (in Russian).

Rearrangements of functions, sign-arrangements and convergence of sequences of
operators, Zapiski Nauchnyh Seminarov LOMI (Leningrad Institute of Mathematics),
107 (1982), 46-70 (in Russian). English translation in the Journal of Soviet Mathemat-
ics,
36, No.3 (1987), 326-341.

Estimates for the Pettis integral in interpolation spaces and some inverse imbed-
ding theorems, Doklady of the USSR Academy of Sciences, 263, No.4 (1982), 793-798
(in Russian). English translation in the Soviet Mathematics Doklady, 25, No.2 (1982),
428-432.

On the singularities of summable functions, Zapiski Nauchnyh Seminarov LOMI
(Leningrad Institute of Mathematics),
113 (1981), 76-96 (in Russian). English trans-
lation in the Journal of Soviet Mathematics, 22, No.6 (1983), 1743-1757.

On the convergence of orthogonal series in L1 and almost everywhere, Bull Geor-
gian Academy of Sciences,
102, No.3 (1981), 541-544 (in Russian).

On the behavior of the Fourier coefficients of equimeasurable functions, Doklady of
the USSR Academy of Sciences,
250, No.4 (1980), 787-790 (in Russian). English trans-
lation in the Soviet Mathematics Doklady, 21, No.1 (1980), 191-194.

On the behavior of the Fourier transform in function spaces, Funktsional’nyi Analiz,
14, No.4 (1980), 71-722 (in Russian).

On the convergence of expansions of rearranged and sign-changed functions, Bul-
letin of the Georgian Academy of Sciences,
96, No.3 (1979), 537-540 (in Russian).

On the behavior of linear operators on the trajectories of elements, Bulletin of the
Georgian Academy of Sciences,
93, No.3 (1979), 549-552 (in Russian).

The individual interpolation theorem, Bulletin of the Georgian Academy of Sciences,
94, No.1 (1979), 33-36 (in Russian).

On the behavior of the Fourier transform of rearranged functions, Bulletin of the
Georgian Academy of Sciences,
87, No.2 (1977), 297-299 (in Russian).

(with V.A. Rodin and E.M. Semenov) The Fourier coefficients of summable func-
tions, Matematicheskii Sbornik, 102, No.3 (1977), 362-372 (in Russian).

The interpolation theorem on subsets, Bulletin of the Georgian Academy of Sciences,
88, No.3 (1977), 545-548 (in Russian).

On the behavior of the Fourier coefficients of equimeasurable functions, Studia
Mathematica,
54 (1975), 117-129 (in Russian).

An interpolation theorem of weak type and the behavior of the Fourier transform
of a function having prescribed Lebesgue sets, Doklady of the USSR Academy of Sci-
ences,
218, No.6 (1974), 1268-1271 (in Russian). English translation in Soviet Mathe-
matics Doklady,
15, No.5 (1974), 1481-1485.

Metric equivalence and Fourier coefficients, Bulletin of the Georgian Academy of Sci-
ences,
94, No.1 (1972), 553-555 (in Russian).

Fourier transforms of monotonic functions and distribution functions, Doklady of
the USSR Academy of Sciences,
196, No.6 1971, 1259-1262 (in Russian). English trans-
lation in Soviet Mathematics Doklady 12, No.1 (1971), 336-340.

Trigonometric series with monotonically decreasing coefficients and distribution
functions, Matematicheskie Zametki, 10, No.1 (1971), 3-10 (in Russian).

Estimates for the distribution functions of trigonometric series with monotonically
decreasing coefficients, Bulletin of the Georgian Academy of Sciences, 58, No.1 (1970),
21-24 (in Russian).

More Publications

Book review on K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in
Math., Vol. 85,
Cambridge: University Press, 1985,– in Algebra and Analysis, 2, No.2
(1990), 249-259 (in Russian).

Book review on David Ruelle, Chaotic Evolution and Strange Attracators, Cambridge:
University Press, 1989, Algebra and Analysis, 3, No. 2 (1991). English translation in
St. Petersburg Math. J., 3, No. 4 (1992), 923-935.

Book review on Selected Papers of Norman Levinson, Birkhäuser, Boston-Basel-
New York, 2 vol., 1998, Annals of the Polish Mathematical Society, s.III, Applied Math-
ematics,
41 (1999), 55-59.

Conversations with Gustave Choquet about his visit to Poland soon after the Sec-
ond World War, Analyse stochastique et theorie du potentiel, Saint Priest de Gimel
(2002), Association Laplace-Gauss, 2003.

Gustave Choquet rozmawia o swoim pobycie w Polsce po II wojnie światowej,
Roczniki Polskiego Towarzystwa Matematycznego, Seria II: Wiadomosci Matematyczne,
39 (2003), 157-164 (translation of the previous item into Polish).

Feynman-Kac propagators and viscosity solutions (with J. A. van Casteren), Cen-
tre de Recerca Matematica Preprint Series, Barcelona, Spain, No 572, April 2004, 17 pages.

Markov processes and Feynman-Kac propagators, Centre de Recerca Matematica
Preprint Series, Barcelona, Spain, No 573, April 2004, 48 pages.


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