
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR

Actuarial
Science and Mathematical Finance Group Meetings 201213
at
the Fields Institute, Stewart Library
Organizer:
Sebastian Jaimungal (U of Toronto)


OVERVIEW
The Actuarial Science and Mathematical Finance research group meets
on a regular basis to discuss various problems and methods that arise
in Finance and Actuarial Science. These informal meetings are held
at the Fields Institute for Mathematical Sciences and are open to
the public. Talks range from original research to reviews of classical
papers and overviews of new and interesting mathematical and statistical
techniques/frameworks that arise in the context of Finance and Actuarial
Science. This seminar series is sponsored in part by Mprime through
the research project Finsurance
: Theory, Computation and Applications.
Meetings are normally held on Thursdays in the Stewart Library,
but check calendar for exceptions. If you are interested in presenting
in this series please contact the seminar organizer: Professor Sebastian
Jaimungal (sebastian [dot] jaimungal [at] utoronto [dot] ca).
Upcoming
Seminars 
TBA


Past Seminars 
Thursday, March 14, 2013
5:00 p.m.
Stewart Library

Takashi Shibata, Tokyo Metroplitan University
Investment timing, debt structure, and financing constraints
We introduce debt issuance limit constraints along with market debt
and bank debt to consider how financial frictions affect investment,
financing, and debt structure strategies. Our model provides four
important results. First, a firm is more likely to issue market debt
than bank debt when its debt issuance limit increases. Second, investment
strategies are nonmonotonic with respect to debt issuance limits.
Third, debt issuance limits distort the relationship between a firm's
equity value and investment strategy. Finally, debt issuance limit
constraints lead to debt holders experiencing low risk and low returns.
That is, the more severe the debt issuance limits, the lower the credit
spreads and default probabilities. Our theoretical results are consistent
with stylized facts and empirical results. This is joint work with
Michi Nishihara, Osaka University.

Tuesday
March 5th
at 5pm.

Mikhail Zhitlukhin, University of Manchester
Disorder detection problems for diffusion processes and their applications
in finance
We consider several questions related to problems of quickest disorder
detection for diffusion processes. By a disorder we mean an unknown
moment of time when the structure of an observable process changes,
e.g. a drift appears. In the first part of the talk we present general
results on the existence of Markov sufficient statistics and show
how disorder detection problems can be reduced to Markovian optimal
stopping problems. In particular, we solve disorder problems for Brownian
motion with a disorder on a finite time segment. In the second part
of the talk we apply the results obtained to practical questions of
choosing the optimal time to sell an asset which initially has a positive
trend and then the trend reverses at some unknown moment of time.
We test our criteria on real market data and show that they give relatively
good results. (This is a joint work with A.N. Shiryaev and W.T. Ziemba.)

Thursday Sept. 20
5:00 p.m.

Mikhail Krayzler (Dept.
Mathematics, Technische Universität München)
Pricing of Guaranteed Minimum Benefits in Variable Annuities
The worldwide market of variable annuities (VAs) has been rapidly
growing since their introduction in the mid1980s in the United States.
These fundlinked annuity products, which have become an essential
part of the retirement plans in many countries, are often combined
with additional living and death benefits. Since they are usually
of a complex nature, consistent pricing of variable annuities becomes
a difficult task. As there is often a tradeoff between a realistic
model and analytical tractability, several studies in the literature
either focus on closedform solutions, by simplifying the contract
setups and the modeling assumptions, or propose numerical methods
for the multifactor models. This work aims to fill this gap by showing
how the explicit representations for prices of some of the VA products
can be derived in a hybrid model for insurance and market risks.

Thursday Sept. 6
5:00 p.m.

Lane Hughston (University College London)
Signal Processing with Lévy Information
Lévy processes, which have stationary independent increments,
are ideal for modelling the various types of noise that can arise
in communication channels. If a Lévy process admits exponential
moments, then there exists a parametric family of measure changes
called Esscher transformations. If the parameter is replaced with
an independent random variable, the true value of which represents
a “message”, then under the transformed measure the original
Lévy process takes on the character of an “information
process”. In this paper we develop a theory of such Lévy
information processes. The underlying Lévy process, which we
call the fiducial process, represents the “noise type”.
Each such noise type is capable of carrying a message of a certain
specification. A number of examples are worked out in detail, including
information processes of the Brownian, Poisson, gamma, variance gamma,
negative binomial, inverse Gaussian, and normal inverse Gaussian type.
Although in general there is no additive decomposition of information
into signal and noise, one is led nevertheless for each noise type
to a welldefined scheme for signal detection and enhancement relevant
to a variety of practical situations. In this presentation we also
consider applications to the theory of finance. (Joint work with Dorje
C. Brody, Brunel University, and Xun Yang, Imperial College London.
The paper can be found at: arxiv.org/abs/1207.4028v1)

Past Seminars 201112
Past Seminars 201011
Past Semainrs 200910
Past Seminars 200809

