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Actuarial Science and Mathematical Finance Group Meetings
2007-08
at the Fields Institute
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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.
Meetings are normally held on Wednesdays from 2pm to 3:30pm, but
check calendar for exceptions.
If you are interested in presenting in this series please contact
the seminar organizer: Prof. Sebastian Jaimungal (sebastian
[dot] jaimungal [at] utoronto [dot] ca).
May 26,
2008
Wednesday
2:00 p.m |
Speaker: Roger Lee, Department of Mathematics, University
of Chicago
Implied Volatility in Relation to Realized Volatility
If realized volatility is a nonrandom constant, then of course
the Black-Scholes implied volatility equals that constant
realized volatility. If realized volatility is random, then
how does it relate to implied volatility? We answer this question
with respect to several notions of implied volatility -- the
Black-Scholes definition, and two model-free definitions.
We start by assuming only the positivity and continuity of
the underlying price paths.
Based on joint work with Peter Carr.
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May 21,
2008
Wednesday
2:00 p.m
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Hans J.H.Tuenter, Energy Markets, Ontario Power Generation
Expected Overshoot in the Case of Normal Variables with
Positive Mean
The expected overshoot in the case of normal variables
with positive mean is studied, and simpler self-contained
derivations of the known results are given. We also give new
series expansions with better convergence properties. Applications
in finance are found in option pricing, where overshoot corrections
have been used in the pricing of discrete barrier options.
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May 7,
2008
Wednesday
2:00 p.m |
Andrei Badescu, Department
of Statistics, University of Toronto
Return Probabilities of Stochastic Fluid Flows and Their
Use in Collective Risk Theory
One way of analyzing insurance risk models is by making
use of the existing connections with stochastic fluid flows.
Matrix-analytic methods constitute a useful approach to the
study of such fluid flow models. In the present talk we illustrate
the derivation of several first passage probabilities whose
numerical calculation is very tractable, based on the structure
and the probabilistic meaning of certain matrices describing
these fluid models. In the end, we enumerate several classes
of risk processes that can be analyzed using these probabilistic
tools. |
Feb 5,
2008
Tuesday
2:00 p.m |
Speaker: Matheus Grasselli,
Department of Mathematics, Mc Master University.
Indifference pricing of insurance contracts: stochastic volatility
and stochastic interest rates
In the first part of this talk I will present an asymptotic
expansion for the indifference price of equity-linked insurance
contracts in when the underlying financial asset follows a
2-factor stochastic volatility model with fast mean reversion.
For the second part of the talk, I consider path-dependent
contracts under stochastic interest rates, obtain optimal
investment strategies using stocks and bonds, and present
integral representations for the price of contracts that depend
exclusively on the paths of interest rates.
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Jan 23,
2008
Wednesday
2:00 p.m |
Speaker: Sebastian Jaimungal,
University of Toronto
Indifference Valuation for Credit Default Swaps through a
Structural Approach
Traditional structural models assume that firm value is a
tradable security and proceed to value defaultable bonds as
European or Barrier options on firm value. We introduce a
model in which default is driven by a visible (but not tradable)
credit worthiness index (CWI) that is correlated to the firm's
equity value. Default occurs when the CWI falls below a critical
level at which time equity drops to zero. Given the incomplete
nature of this market setting, we adopt stochastic optimal
control methods through utility indifference to extract the
implied bond values and CDS spreads.
[ joint work with Georg Sigloch ]
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Nov 30,
2007
Friday
2:00 p.m. |
Speaker: Erhan Bayraktar,
Department of Mathematics, University of Michigan.
Pricing Asian Options for Jump Diffusions
In this talk, I will discuss the pricing problem for the
European Asian options in jump diffusion models. Following
the method I used to solve the problem for American options,
a sequence of functions are also constructed to approximate
the price of Asian options. However, because the pay-off functions
are not necessarily bounded, new methods are introduced to
prove the regularity of functions in this sequence. As a result,
this sequence of functions converge unformly and exponentially
fast to the price of Asian option on compact sets. This provides
us a fast numerical algorithm. At the end of this talk, I
will present the numerical performance of this algorithm for
Merton's model and Kou's model.
Joint work with Hao Xing.
Relevant papers are available at: http://arxiv.org/abs/0707.2432,m
http://arxiv.org/abs/math.OC/0703782
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Nov 7, 2007
Wednesday
2:00 p.m
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Speaker: Marcel Rindisbacher, Rotman Business School,
University of Toronto
Dynamic Asset-Liability Management for Defined-Benefit
Pension Plans
A dynamic asset-liability management model for defined-benefit
pension plans is developed. The plan sponsor exhibits features
of loss aversion and tolerance for limited shortfalls in assets
under management relative to the liability due. The optimal
contribution policy, the optimal dividend policy and the associated
asset allocation rule are derived and analyzed. Sound Asset-Liability
Management is shown to entail withdrawals as well as contributions
from the pension fund.
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Oct. 31, 2007
Wednesday
2:00 p.m |
Speaker: Marcel Rindisbacher, Rotman Business School,
University of Toronto
Monte Carlo Methods for Optimal Portfolios
This talk provides an introduction and short overview on some
recent Monte Carlo Methods to solve optimal dynamic asset
allocation problems. Using the martingale approach and elements
from Malliavin calculus, a fully
probabilistic representation of the optimal portfolio policy
is derived. This representation is of the Feynman-Kac type
and therefore key to formulateMonte Carlo methods. The Malliavin
method is compared with alternative Monte
Carlo techniques that do not rely on an exact probabilistic
representation. Finally, the Malliavin Monte Carlo method
is illustrated with several examples.
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Oct.
3,2007
Wednesday
2:00 p.m |
Speaker: Michael Walker, Department of Physics, University
of Toronto
Calibration, the Timing of Defaults, and the Marking to
Market of CDO's
The talk begins with a qualitative description of CDO's
and their usefulness in helping banks to shed the default
risk of a loan portfolio. Then the iTraxx and CDO markets
for CDO's are described. For these markets, there are a large
number of market prices for CDO contracts of different maturities
and different tranches established for a given underlying
portfolio on a given day. The problem of calibrating a model
to this large number of market prices has been one of the
central problems of CDO research, and the loss surface approach
to calibration is described.
The impact of calibration across maturities on the determination
of the timing of defaults is discussed, as is the impact of
the timing of defaults on the marking to market of CDO contracts.
In so far as time permits, an introduction to the extension
of the loss surface model to a dynamic model, capable of being
calibrated to dynamics-sensitive contracts such as options
on CDO's and leveraged super-senior tranches, will be given.
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Sept. 14,
2007
Friday |
Speaker: Michael Ludkovski,
Dept Mathemtics, University of Michigan
Relative Hedging of Systematic Mortality Risk
I will first review recent models of stochastic mortality
and the associated problems in pricing mortality contingent
claims under stochastic mortality age structures. The focus
of my talk will then be on capturing the internal population-level
cross-hedge between components of an insurer's portfolio,
especially between life annuities and life insurance. I will
derive and compare several linear mechanisms which value claims
under various martingale measures, and then pass to exhaustive
analysis of the exponential premium principle which is the
representative nonlinear pricing rule in this framework. The
results will be illustrated with a couple of numerical examples
that show the relative importance of model parameters. Based
on joint work with Erhan Bayraktar and Jenny Young (U of Michigan).
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