ICE-EM Workshop on Mathematical Methods in Finance
Melbourne September 25 and 26, 2006
5th National Symposium on Financial Mathematics
Melbourne September 27, 28 and 29, 2006
To be held at the AMSI Offices, Ground Floor, ICT Building, 111 Barry Street, Carlton
Generously supported by
International Centre of Excellence for Education in Mathematics
Australian Mathematical Sciences Institute
Financial Integrity Research Network
Centre for Modelling of Stochastic Systems at Monash University
ICE-EM is managed by:
ICE-EM is funded by the Australian Government through the Department of Education, Science and Training and
managed by the Australian Mathematical Sciences Institute (AMSI).
Organising Committee
Chris Heyde
o Australian National University
Fima Klebaner
o Monash University
Eckhard Platen
o University of Technology, Sydney
Local Organising Committee
Kais Hamza
o Monash University
Fima Klebaner
o Monash University
ICE-EM Workshop on Mathematical Methods in Finance
Monday 25 September 2006
8:30
9:00
10:30
11:00
12:30
2:00
3:30
4:00
5:00
6:00
– 9:00 Registration
– 10:30 Freddy Delbaen
Dynamic Risk Measures Leading to Backward Stochastic Differential Equations
Lecture Theatre 2
Lecture 1
AMSI Offices
– 11:00 Coffee Break
– 12:30 Freddy Delbaen
Dynamic Risk Measures Leading to Backward Stochastic Differential Equations
Lecture Theatre 2
Lecture 2
– 2:00 Lunch Break
– 3:30 Freddy Delbaen
Dynamic Risk Measures Leading to Backward Stochastic Differential Equations
Lecture Theatre 2
Lecture 3
AMSI Offices
– 4:00 Coffee Break
– 5:00 Freddy Delbaen
Dynamic Risk Measures Leading to Backward Stochastic Differential Equations
Lecture Theatre 2
Lecture 4
– 6:00 Freddy Delbaen
Dynamic Risk Measures Leading to Backward Stochastic Differential Equations
Lecture Theatre 2
Tutorial
AMSI Offices
– 7:00 Wine & Cheese Discussion
Tuesday 26 September 2006
9:00
10:30
11:00
12:30
2:00
3:30
4:00
5:00
6:00
– 10:30 Uwe Küchler
Stochastic Differential Delay Equations
Lecture 1
– 11:00 Coffee Break
– 12:30 Uwe Küchler
Stochastic Differential Delay Equations
Lecture 2
– 2:00 Lunch Break
– 3:30 Valentina Dragan
Credit Risk Modelling
Lecture 1
– 4:00 Coffee Break
– 5:00 Valentina Dragan
Credit Risk Modelling
Lecture 2
– 6:00 Valentina Dragan
Credit Risk Modelling
Tutorial
– 8:00 Reception
Lecture Theatre 2
AMSI Offices
Lecture Theatre 2
Lecture Theatre 2
AMSI Offices
Lecture Theatre 2
Lecture Theatre 2
Outside Lecture Theatre 3
2nd Floor
ICE-EM Workshop on Mathematical Methods in Finance
Monday, all day
Dynamic Risk Measures Leading to Backward Stochastic Differential
Equations
Freddy Delbaen
The theory of monetary utility functions can be extended to a dynamic framework on condition to
require "time consistency". This property -- introduced by Koopmans in 1960 – was seen to be
equivalent to other conditions. We extend the basic work of Epstein, Schneider and Zinn to
continuous time and general probability spaces. We also show that the time consistency is
equivalent to a decomposition property for the convex set of acceptable elements as well as to a
Bellman principle and a submartingale characterisation.
ICE-EM Workshop on Mathematical Methods in Finance
Tuesday, morning
Stochastic Differential Delay Equations
Uwe Küchler
Stochastic Delay Differential Equations (SDDE's) describe time dependent random phenomena
where the future development is influenced also by the past of the process. A typical SDDE is given
by dX (t ) =
µ (t , X t )dt + σ (t , X t )dW (t ) , t ≥ 0 , where W (⋅) is a Wiener process and
X t = ( X (t + s ), s ∈ [−r ,0]) denotes the ''segment'' of X (⋅) of ''memory''-length r > 0 at time t .
SDDE's frequently appear in mathematical models of real world processes, in particular in biology
and economics.
The talk mainly treats affine SDDE's of the type
0
dX (t ) = − ∫ X (t + s )a (ds )dt + dW (t ) , t ≥ 0
−r
where a (⋅) is an arbitrary signed finite measure on [− r ,0] . Properties of the solution process
X (⋅) and estimation procedures for a(⋅) are studied. Applications to nonlinear SDDE's are
discussed.
Selected References:
Gushchin, A.A., Küchler, U., Asymptotic Properties of Maximum-Likelihood-Estimatiors for a Class
of Linear Stochastic Differential Equations with Time Delay. Bernoulli 5(6) (1999), 1059–1098.
Gushchin, A. A., Küchler, U., On Stationary Solutions of Delay Differential Equations Driven by a
L\'evy Process. Stochastic Processes and their Applications 88, (2000), 195–211.
Küchler, U., Mensch, B., On Langevins stochastic differential equation extended by a time delayed
term. Stochastics and Stochastic Reports 40, (1991), 123–144.
Küchler, U., Platen, E., Strong Discrete Time Approximation of Stochastic Differential Equations
with Time Delay. Mathematics and Computer Simulation 54 (2000), 189–205.
Küchler, U., Platen, E., Weak Discrete Time Approximation of Stochastic Differential Equations with
Time Delay. Mathematics and Computer Simulations. (2002) 59, 497–507.
Küchler, U., Vassiliev,V., Sequential identification of linear dynamic systems with memory.
Statistical Inference of Stochastic Processes (2005) VIII, (1), p. 1–24.
Mao, X., (1997) Stochastic Differential Equations and Applications, Horwood
ICE-EM Workshop on Mathematical Methods in Finance
Tuesday, afternoon
Credit Risk Modelling
Valentina Dragan
TBA
5th National Symposium on Financial Mathematics
Wednesday 27 September 2006
9:00
9:30
10:30
11:00
11:45
12:30
2:00
2:45
3:30
4:00
4:30
7:00
– 9:30 Registration
– 10:30 Freddy Delbaen
Characterisation of b(M) for continuous BMO
martingales
– 11:00 Coffee Break
– 11:45 Daniel Dufresne
Stochastic life annuities
– 12:30 Mark Joshi
Upper bounds for early exercisable derivatives in Monte
Carlo simulations: extending and refining
Rogers/Haugh-Kogan and Jamshidian
– 2:00 Lunch Break
– 2:45 Jerzy Filar
Time consistent dynamic risk measures
– 3:30 Uwe Kuechler
Bilateral gamma distributions and processes in financial
mathematics
– 4:00 Coffee Break
– 4:30 Hardy Hulley
A survey and reassessment of the constant elasticity of
variance model
– 5:00 Nicola Bruti Liberati
Weak predictor-corrector methods for jump diffusions in
finance
– 10:00 Dinner
Plenary Talk
Lecture Theatre 2
AMSI Offices
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
AMSI Offices
Contributed Talk
Lecture Theatre 2
Contributed Talk
Lecture Theatre 2
Borsari, 201 Lygon Street,
Carlton
ICE-EM Workshop on Mathematical Methods in Finance – Supplementary Session
5:00
–
6:00 Uwe Küchler
Stochastic Differential Delay Equations
Tutorial
Lecture Theatre 2
5th National Symposium on Financial Mathematics
Thursday 28 September 2006
9:45
10:30
11:00
11:45
12:30
2:00
2:45
3:30
4:00
4:30
5:00
– 10:30 Fima Klebaner
Non-constant volatility in Black-Scholes
– 11:00 Coffee Break
– 11:45 Ben Goldys
Stochastic volatility models and short time asymptotics of
implied volatilities
– 12:30 Kais Hamza
A family of non-Gaussian martingales with Gaussian
marginals
– 2:00 Lunch Break
– 2:45 Kostya Borovkov
Stochastic difference equations and growing annuities
under stochastic interest rates
– 3:30 Boris Miller
Generalized (discontinuous) solutions in stochastic
control problems
– 4:00 Coffee Break
– 4:30 Gunardi
P(I)DE approach for Indonesian options pricing
– 5:00 Neda Zamani
Mechanical vs. informational components of price impact
– 5:30 Charles Li
An Improved EM Algorithm and Semi-Blind Channel
Identification for Affinely Precoded Communication
Systems
Invited Talk
Lecture Theatre 2
AMSI Offices
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
AMSI Offices
Contributed Talk
Lecture Theatre 2
Contributed Talk
Lecture Theatre 2
Contributed Talk
Lecture Theatre 2
Friday 29 September 2006
9:45
10:30
11:00
11:45
12:30
2:00
3:30
– 10:30 Boris Buchmann
A Poisson song: non-parametric inference for pure-jump
Levy processes
– 11:00 Coffee Break
– 11:45 Erik Schlögl
Generic implementation of control variates in option
pricing
– 12:30 Truc Le
Approximating the growth optimal portfolio with a
diversified World Stock Index
– 2:00 Lunch Break
– 3:00 Eckhard Platen
On the pricing and hedging of long dated zero coupon
bonds
– 4:00 Coffee Break
Invited Talk
Lecture Theatre 2
AMSI Offices
Invited Talk
Lecture Theatre 2
Invited Talk
Lecture Theatre 2
Plenary Talk
Lecture Theatre 2
AMSI Offices
5th National Symposium on Financial Mathematics
Wednesday, 9:30-10:30
Characterisation of b(M) for continuous BMO martingales
Freddy Delbaen
The dual problem is equivalent to the Föllmer-Schweizer decomposition and the results clarify the
results of (Delbaen-Monat-Schacehrmayer-Schweizer-Stricker for the case p=2) as well as the
extension to arbitrary exponents by Grandits and Krawczyk. The study of the differential equation
leads to a characterisation of the parameter b(M) for continuous BMO martingales. There is a need
to treat stochastic exponentials for complex valued martingales in order to see b(M) as being
bounded (above and below) by the spectral radius of an operator.
This is joint work with Prof. Tang (Fudan University Shanghai).
5th National Symposium on Financial Mathematics
Wednesday, 11:00-11:45
Stochastic life annuities
Daniel Dufresne
A person retires at some age r, and receives a pension (of some fixed annual amount y) from a
fund initially worth F. The fund is invested on the stock market, and has returns generated by a
Brownian motion. A question of practical interest is: "What is the probability that the amount F will
be sufficient to provide the pension until the end of the life of the individual?" This question
appeared in the actuarial literature more than three decades ago, but until now only moments of the
discounted value of the pension (or "annuity") had been calculated. The paper answers the
previous question by giving an analytic approximation for the distribution of this "stochastic life
annuity". The approximation is based on (1) a result due to Yor about the integral of geometric
Brownian motion, and (2) the expression of a distribution of the positive half-line by a limit of
combinations of exponentials.
5th National Symposium on Financial Mathematics
Wednesday, 11:45-12:30
Upper bounds for early exercisable derivatives in Monte Carlo
simulations: extending and refining Rogers/Haugh-Kogan and
Jamshidian
Mark Joshi
A person retires at some age r, and receives a pension (of some fixed annual amount y) from a
fund initially worth F. The fund is invested on the stock market, and has returns generated by a
Brownian motion. A question of practical interest is: "What is the probability that the amount F will
be sufficient to provide the pension until the end of the life of the individual?" This question
appeared in the actuarial literature more than three decades ago, but until now only moments of the
discounted value of the pension (or "annuity") had been calculated. The paper answers the
previous question by giving an analytic approximation for the distribution of this "stochastic life
annuity". The approximation is based on (1) a result due to Yor about the integral of geometric
Brownian motion, and (2) the expression of a distribution of the positive half-line by a limit of
combinations of exponentials.
5th National Symposium on Financial Mathematics
Wednesday, 2:00-2:45
Time consistent dynamic risk measures
Jerzy Filar
We consider a multi-stage portfolio optimization problem where an investor sets himself a fixed
target level x and wishes to minimize the probability that his accumulated total return fails to exceed
that target. We call this problem a target-percentile portfolio allocation problem.
We introduce a time consistency concept that is inspired by the so-called “principle of optimality” of
dynamic programming. We demonstrate that an optimal portfolio allocation policy – in our targetpercentile problem – can be constructed by a backward recursion algorithm. This policy will also be
time consistent with respect to the above concept. Hence, we argue that the corresponding “targetpercentile” risk measure is time consistent and hence more suitable in the multi-stage investment
context. Finally, we demonstrate – via an example – that the conditional value-at-risk (and hence
also value-at-risk) need not be time consistent in a multi-stage setting.
5th National Symposium on Financial Mathematics
Wednesday, 2:45-3:30
Bilateral gamma distributions and processes in financial mathematics
Uwe Küchler
If X and Y are independent Gamma distributed random variables, then X-Y is said to have a
bilateral Gamma distribution (BGD). BGD's form a subclass of so-called tempered stable
distributions. Analytical and statistical properties of BGD's and the associated Lévy processes are
studied. We investigate an exponential Lévy stock model as well as a term structure model with
driving bilateral Gamma processes. The results are applied to real financial data (DAX 1996 1998).
References:
Cont, R., Tankov, P., Financial modelling with jump processes. Chapman and Hall/CRC Press,
London.
Küchler, U., Naumann, E., Markovian short rates in a forward rate model with a general class of
Lévy process. Discussion Paper 6-2003, Sonderforschungsbereich 373, Humboldt-Universität
zu Berlin.
Küchler, U., Tappe, S., Bilateral Gamma Distributions and Processes in Financial Mathematics.
Preprint 2006-12, Math.-Nat. Fakultät II, Humboldt-Universität zu Berlin.
5th National Symposium on Financial Mathematics
Wednesday, 4:00-4:30
A survey and reassessment of the constant elasticity of variance
model
Hardy Hulley
We are interested in parsimonious models of equity indices that capture certain stylized features of
these processes. For example, it is commonly accepted that a good stochastic model for the
dynamics of such an index should exhibit the leverage effect (i.e. the widely perceived inverse
relationship between index level and volatility) as an emergent feature. A natural candidate for
modelling equity indices – by now fairly classical – is the constant elasticity of variance (CEV)
process:
dSt = µ (t ) St dt + σ (t ) Stγ dWt
where
µ (⋅)
and
σ (⋅)
(*)
are time-varying and deterministic, and W is a standard Brownian motion. It
serves as an important reference point, for purposes of comparison, in our search for a good
model.
Following [DS02], we identify a weak solution of (*), expressed as a scaled and time-transformed
squared Bessel process with absorption at zero. Using the transition density of a squared Bessel
process with absorption at the origin, which is easily determined, we derive convenient formulas for
European options on the index. Although the CEV model is well established – dating back to a
research note by Cox, first circulated in 1975 and later published as [Cox96] – the published
literature on the model appears to harbour some anomalies and misconceptions. For example, the
call option pricing formula derived in [EM82] for
γ >1
(and widely quoted elsewhere – see e.g.
[DL01, Hul03, Sch89]) appears to be in error. This is a consequence of the strict supermartingale
nature of the discounted CEV process under the risk-neutral measure, for this parameter regime.
Although the impact of the strict supermartingale property is starting to become topical, its
implications are, in general, probably not that well understood. We demonstrate its culpability in the
break-down of a number of standard relationships, such as put-call parity.
References:
[Cox96] John C. Cox, The constant elasticity of variance option pricing model, The Journal of
Portfolio Management (1996), 15–17, Special issue.
[DL01] Dmitry Davidov and Vadim Linetsky, Pricing and hedging path-dependent options under the
CEV process, Management Science 47 (2001), no. 7, 949–965.
[DS02] Freddy Delbaen and Hiroshi Shirakawa, A note on option pricing for the constant elasticity
of variance model, Asia-Pacific Financial Markets 9 (2002), no. 2, 85–99.
[Eks03] Eric EkstrÄom, Perpetual American put options in a level-dependent volatility model,
Journal of Applied Probability 40 (2003), 783–789.
[EM82] David C. Emanuel and James D. MacBeth, Further results on the constant elasticity of
variance call option pricing model, Journal of Financial and Quantitative Analysis 17 (1982), no.
4, 533–554.
[Hul03] John C. Hull, Options, Futures, and Other Derivative Securities, fifth ed., Prentice Hall,
2003.
[Sch89] Mark Schroder, Computing the constant elasticity of variance option pricing formula, The
Journal of Finance 44 (1989), no. 1, 211–219.
5th National Symposium on Financial Mathematics
Wednesday, 4:30-5:00
Weak predictor-corrector methods for jump diffusions in finance
Nicola Bruti Liberati
Event-driven uncertainties such as corporate defaults, operational failures or central bank
announcements are important elements in the modelling of financial quantities. Therefore,
stochastic differential equations (SDEs) of jump-diffusion type are often used in finance. We
consider in this paper weak discrete time approximations of jump-diffusion SDEs which are
appropriate for problems such as derivative pricing and evaluation of moments, risk measures and
expected utilities. We present regular and jump-adapted predictor-corrector methods with first and
second order of weak convergence. The former are constructed on time discretizations that do not
include jump times, while the latter are based on time discretizations that include all jump times. A
numerical analysis of the accuracy of these methods when applied to the Merton jump-diffusion
model is provided.
5th National Symposium on Financial Mathematics
Thursday, 9:45-10:30
Non-constant volatility in Black-Scholes
Fima Klebaner
We prove that the only model for which implied volatility depends on maturity and current time
compatible with Black-Scholes formula is the Black-Scholes model. In a recent paper, the authors
show that models with non-constant implied volatility
θ t , assumed to be a function (possibly
random) of time t , are not compatible with the Black-Scholes formula. In this paper this conclusion
is generalized for models in which implied volatility is also allowed to depend on maturity T .
References:
Hamza, K., Klebaner, F., On nonexistence of non-constant volatility in the Black-Scholes formula.
Discrete and Continuous Dynamical Systems, 6 (2006), 829–834.
5th National Symposium on Financial Mathematics
Thursday, 11:00-11:45
Stochastic volatility models and short time asymptotics of implied
volatilities
Ben Goldys
In this talk we will present the so-called Market Model of Implied Volatility introduced in the paper by
Brace, Goldys, Klebaner and Womersley. Some fundamental regularity conditions for this model
will be discussed and the related of well-posedness of an associated stochastic partial differential
equation.
5th National Symposium on Financial Mathematics
Thursday, 11:45-12:30
A family of non-Gaussian martingales with Gaussian marginals
Kais Hamza
We construct a family of non-Gaussian martingales the marginals of which are all Gaussian. We
give the predictable quadratic variation of these processes and show they do not have continuous
paths. These processes are Markovian and inhomogeneous in time, and we give their infinitesimal
generators. Within this family we find a class of piecewise deterministic pure jump processes and
describe the laws of jumps and times between the jumps.
5th National Symposium on Financial Mathematics
Thursday, 2:00-2:45
Stochastic difference equations and growing annuities under
stochastic interest rates
Kostya Borovkov
We consider stochastic difference equations (SdE) and related mathematical models for annuities
with payments progressing in a geometric manner. In particular, we analyse the asymptotic
behaviour (as the life-time of the annuity increases) of the distribution of the discounted value of an
annuity with payments growing at a “mean” interest rate, when interest rates are modelled by an
SdE. Moreover, we are looking at the effect of risk sharing when the annuity payments are made by
the reinsurer in case of “underperforming” interest rates.
5th National Symposium on Financial Mathematics
Thursday, 2:45-3:30
Generalized (discontinuous) solutions in stochastic control problems
Boris Miller
Stochastic systems with impulsive or singular controls constitute a very important class of dynamic
systems where the application of the control actions causes very fast (almost abrupt) changes in
the system state. They arise in various areas of applications including: flight dynamics, medicine,
information processes, queuing systems, power production control, stocks management and
mathematical financing. Whereas the theory for general deterministic systems with nonlinear
impulsive and ordinary controls was developed during recent 20 years and discovered a lot of
applications in different fields, in stochastic settings only few problems and only for systems with
linear dependence on impulse controls were solved until now. The reason of that is the nonrobustness of general nonlinear impulse control systems which becomes apparent as the paths
instability with respect to variation of impulse controls, failure of approximation of the impulse
controls by ordinary ones, absence of the optimal controls, and difficulty of the application of direct
variational methods. In this talk the class of robust nonlinear stochastic systems is considered, and
the necessary and sufficient conditions of robustness were given. Basing on these conditions it
becomes possible to solve the variety of problems including: the obtaining of solution
representation in the form of nonlinear stochastic differential equation with a measure, proof the
existence of the optimal generalized solution and the optimal singular (impulsive) control, derive the
optimality conditions for singular controls in the maximum principle form.
5th National Symposium on Financial Mathematics
Thursday, 4:00-4:30
P(I)DE approach for Indonesian options pricing
Gunardi
Jakarta Stock Exchange Indonesia has started to trade Indonesian options at September 9th, 2004.
An Indonesian option can be considered as an American style barrier option with immediate
(forced) exercise if the price hits or crosses the barrier before maturity. The payoff of the option is
based on a moving average of the price of the underlying stock. The barrier is fixed at the strike
price plus or minus a 10 percent. The option is automatically exercised when the underlying stock
hits or crosses the barrier and the difference between strike and barrier is paid immediately. We will
refer to this type of option as an Indonesian option. In this paper we study the pricing of the
Indonesian option under Black-Scholes model by PDE approach and under Variance Gamma
model by PIDE approach.
5th National Symposium on Financial Mathematics
Thursday, 4:30-5:00
Mechanical vs. informational components of price impact
Neda Zamani
When agents hold private information, prices provide a means for individual agents to learn about
the views of others. In financial markets agents act on information by placing trading orders. In turn
this influences prices – buy orders tend to drive the price up, and sell orders tend to drive it down.
But how does one measure the influence of prices on decision making? To address this question
we define the mechanical impact of a trading order as the change in future prices in the absence of
any future changes in decision-making, and the informational impact on future prices as the
remainder. Using order book data from the off-book market of the London Stock Exchange we
show that it is possible to separate mechanical and informational price impacts. The average
mechanical impact of a market order decays with time at a rate that is asymptotically consistent
with a power law with an exponent of roughly 1.5. In contrast, over the time scale of our study, the
average informational impact builds to approach a constant value. Informational impact is positively
if weakly correlated to mechanical impact. This supports the view that the price is indeed
informative: As each trade is placed it generates a temporary mechanical impact, which causes
changes in future order placement, giving the net effect of a permanent change in views about
prices.
5th National Symposium on Financial Mathematics
Thursday, 5:00-5:30
An Improved EM Algorithm and Semi-Blind Channel Identification for
Affinely Precoded Communication Systems
Charles Li
This paper studies the problem of identifying and deconvolving a signal-input signal-output (SISO)
finite impulse response (FIR) channel. Algebraic redundancy is introduced by precoding the signal
prior to transmission. Semi-blind identification algorithm is derived where the EM algorithm is the
major technique to identify the channel parameter with the additive noise assumed to be Gaussian.
However, EM algorithm often converges very slowly due to statistical property of the algorithm
itself. Quite surprisingly, channel models used in communication systems often exploit some
geometric structure. This paper derived the problem of channel estimation problem with the
parameter space naturally a projective space which is a smooth manifold. A steepest decent
method on projective space is derived with comparison of usual one. Convergence properties is
also studied in this paper.
5th National Symposium on Financial Mathematics
Friday, 9:45-10:30
A Poisson song: non-parametric inference for pure-jump Levy
processes
Boris Buchmann
Given observations from a Levy process, we provide a nonparametric estimator for its Levy
measure. Weighted uniform confidence bounds are constructed. To this end, necessary and
sufficient conditions are discussed to characterize possible weights in a class of functions. The
bootstrap principle is established and some modifications of the sampling scheme are given to deal
with the possible infinite activity.
5th National Symposium on Financial Mathematics
Friday, 11:00-11:45
Generic implementation of control variates in option pricing
Erik Schlögl
Given observations from a Levy process, we provide a nonparametric estimator for its Levy
measure. Weighted uniform confidence bounds are constructed. To this end, necessary and
sufficient conditions are discussed to characterize possible weights in a class of functions. The
bootstrap principle is established and some modifications of the sampling scheme are given to deal
with the possible infinite activity.
5th National Symposium on Financial Mathematics
Friday, 11:45-12:30
Approximating the growth optimal portfolio with a diversified World
Stock Index
Truc Le
This paper constructs and compares various total return world stock indices based on daily data of
regional stock market indices. Due to diversification these indices are noticeably similar. A
diversification theorem identifies any diversified portfolio as a proxy of the growth optimal portfolio.
This is the portfolio that maximizes expected logarithmic utility and after a sufficiently long time
outperforms all other strictly positive portfolios almost surely. Under the benchmark approach, the
paper constructs an investable, diversified world stock index that outperforms the other considered
indices and argues that it is a good proxy of the growth optimal portfolio. Such a proxy facilitates
applications of the benchmark approach in derivative pricing and investment management.
5th National Symposium on Financial Mathematics
Friday, 2:00-3:00
On the pricing and hedging of long dated zero coupon bonds
Eckhard Platen
The pricing and hedging of long dated zero coupon bonds is a challenging area of research. As a
result of utility indifference pricing for general payoffs the growth optimal portfolio turns out to be the
appropriate numeraire or benchmark with the real world probability measure as corresponding
pricing measure. This concept of real world pricing can be applied for valuing long dated derivative
contracts. An equivalent risk neutral probability measure does not need to exist under the
benchmark approach. This paper uses a diversified world stock index as proxy for the growth
optimal portfolio. It develops a parsimonious model for the index dynamics, which is based on a
time transformed squared Bessel process. Surprisingly low prices for long dated zero coupon
bonds result that can be replicated using historical data. Such prices and hedges are difficult to
explain under the prevailing risk neutral approach.
List of Speakers
ICE-EM Workshop on Mathematical Methods in Finance
Delbaen, Freddy
Dragan, Valentina
Küchler, Uwe
Dynamic Risk Measures Leading to Backward Stochastic
Differential Equations
Credit Risk Modelling
Stochastic Differential Delay Equations
Mon all day
Tue pm
Tue am
5th National Symposium on Financial Mathematics
Borovkov, Kostya
Bruti Liberati, Nicola
Buchmann, Boris
Delbaen, Freddy
Dufresne, Daniel
Filar, Jerzy
Goldys, Ben
Gunardi
Hamza, Kais
Hulley, Hardy
Joshi, Mark
Klebaner, Fima
Küchler, Uwe
Le, Truc
Li, Charles
Miller, Boris
Platen, Eckhard
Schlögl, Erik
Zamani, Neda
Stochastic difference equations and growing annuities under
stochastic interest rates
Weak predictor-corrector methods for jump diffusions in finance
A Poisson song: non-parametric inference for pure-jump Levy
processes
Characterisation of b(M) for continuous BMO martingales
Stochastic life annuities
Time consistent dynamic risk measures
Stochastic volatility models and short time asymptotics of
implied volatilities
P(I)DE approach for Indonesian options pricing
A family of non-Gaussian martingales with Gaussian marginals
A survey and reassessment of the constant elasticity of variance
model
Upper bounds for early exercisable derivatives in Monte Carlo
simulations: extending and refining Rogers/Haugh-Kogan and
Jamshidian
Non-constant volatility in Black-Scholes
Bilateral gamma distributions and processes in financial
mathematics
Approximating the growth optimal portfolio with a diversified
World Stock Index
An Improved EM Algorithm and Semi-Blind Channel
Identification for Affinely Precoded Communication Systems
Generalized (discontinuous) solutions in stochastic control
problems
On the pricing and hedging of long dated zero coupon bonds
Generic implementation of control variates in option pricing
Mechanical vs. informational components of price impact
Thu 2.00
Wed 4.30
Fri 9.45
Wed 9.30
Wed 11.00
Wed 2.00
Thu 11.00
Thu 4.00
Thu 11.45
Wed 4.00
Wed 11.45
Thu 9.45
Wed 2.45
Fri 11.45
Thu 5.00
Thu 2.45
Fri 2.00
Fri 11.00
Thu 4.30
List of Participants
Name
Institution
Email
Mark Aarons
Manuel Arapis
Damien Bankovsky
Kostya Borovkov
Nicola Bruti Liberati
Boris Buchmann
Freddy Delbaen
Binh Do
Andrew Downes
Valentina Dragan
Daniel Dufresne
Wendy Ensink
Jerzy Filar
Ben Goldys
Gunardi Gunardi
Kais Hamza
Hardy Hulley
Mark Joshi
Ben Kaehler
Fima Klebaner
Uwe Kuechler
Truc Le
Chi (Charles) Li
Sue Liang
Ashley Lim
Ngo Hoang Long
Iain MacLachlan
Boris Miller
Phan Trong Nghia
Lei Pan
Tin Yan PANG
Jane Paterson
Tao Peng
Katharine Pierce
Eckhard Platen
Michael Roper
Adam Rosenow
Jocelyn San Pedro
Erik Schlogl
Sergei Schreider
Ankur Sharda
Peter Sokolowski
Abby Tan
Miriam Thomas
Daniel Tokarev
Tran Quang Vinh
Warren Volk-Makarewicz
Chit Wai Wong
Henry Wong
Bohr F. Yeh
Martin Yick
Neda Zamani
National Australia Bank
University of Western Australia
Australian National University
University of Melbourne
University of Technology, Sydney
Australian National University
ETH Zurich
Monash University
mark.aarons@nab.com.au
Manuel.Arapis@dtf.wa.gov.au
damien.bankovsky@maths.anu.edu.au
K.Borovkov@ms.unimelb.edu.au
Nicola.Brutiliberati@uts.edu.au
Boris.Buchmann@maths.anu.edu.au
delbaen@math.ethz.ch
binh.do@buseco.monash.edu.au
an_downes@yahoo.com.au
draganv@anz.com
dufresne@unimelb.edu.au
w.ensink@pgrad.unimelb.edu.au
Jerzy.Filar@unisa.edu.au
beng@maths.unsw.edu.au
gunardi@ugm.ac.id
Kais.Hamza@sci.monash.edu.au
Hardy.Hulley@uts.edu.au
mark.joshi@unimelb.edu.au
kaehler@maths.anu.edu.au
fima.klebaner@sci.monash.edu.au
kuechler@mathematik.hu-berlin.de
Tructn.Le@uts.edu.au
Charles.Li@rsise.anu.edu.au
sue_liang22@hotmail.com
Ashley.Lim@sci.monash.edu.au
lenhholong@yahoo.com
maclachl@anz.com
boris.miller@sci.monash.edu.au
ptnghia@mathdep.hcmuns.edu.vn
ln@deakin.edu.au
iantinpang@yahoo.com.hk
jane.paterson@nab.com.au
Tao.Peng-1@student.uts.edu.au
katharine.pierce@nicta.com.au
eckhard.platen@uts.edu.au
mproper@maths.unsw.edu.au
arosenow@students.latrobe.edu.au
Jocelyn.San.Pedro@nab.com.au
Erik.Schlogl@uts.edu.au
kirsten.millman@rmit.edu.au
sharda01@student.uwa.edu.au
petersok@iinet.net.au
drtan@fos.ubd.edu.bn
miriam.thomas@sci.monash.edu.au
Daniel.Tokarev@sci.monash.edu.au
vinhtq@dhsphn.edu.vn
w.volk-makarewicz@ugrad.unimelb.edu.au
c.wong2@pgrad.unimelb.edu.au
Henry_L_Wong@national.com.au
f.b.yeh@math.thu.edu.tw
h9946514@hkusua.hku.hk
neda@cs.usyd.edu.au
ANZ Bank
University of Melbourne
University of Melbourne
University of South Australia
University of New South Wales
University of Gadjah Mada
Monash University
University of Technology, Sydney
University of Melbourne
Australian National University
Monash University
Humboldt University Berlin
University of Technology, Sydney
Australian National University
RMIT University
Monash University
Hanoi Institute of Mathematics
ANZ Bank
Monash University
University of Natural Sciences
School of IT, Deakin University
Macquarie University
National Australia Bank Limited
University of Technology, Sydney
National ICT Australia
University of Technology, Sydney
University of New South Wales
La Trobe University
National Australia Bank
University of Technology, Sydney
RMIT University
University of Western Australia
University of Newcastle
Universiti Brunei Darussalam
Monash University
Monash University
Hanoi Institute of Mathematics
University of Melbourne
University of Melbourne
National Australia Bank
Tunghai University
University of Hong Kong
University of Sydney